Alligations

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Alligations

After completing t

After completing this chapter, youhis chapter, you should be able to:

should be able to:

•

•UnderUnderstand wstand when to use thhen to use thee alligation principle for

alligation principle for calculations.

calculations. •

•CalculCalculate a varietate a variety of alligatiy of alligation- on-related problems.

INTRODUCTION

Alligations are used when mixing two products with different Alligations are used when mixing two products with different percent strengths of the same active ingredient. The strength percent strengths of the same active ingredient. The strength of the final product will fall between the strengths of each of the final product will fall between the strengths of each original product.

original product.

L

earning Objectives

CHAPTER

7

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Solving Alligations

You can use the alligation method to determine how many parts of the same You can use the alligation method to determine how many parts of the same product, with different strengths, you will need to create the final strength product, with different strengths, you will need to create the final strength requested. Further, you can calculate exactly how many milliliters or grams requested. Further, you can calculate exactly how many milliliters or grams you need of

you need of each beginning product.each beginning product.

The Alligation Grid

% % Higher Strength Higher Strength % % Desired Desired Number/Parts of Number/Parts of Higher Strength Higher Strength Number/Parts of Number/Parts of Lower Strength Lower Strength % % Lower Strength Lower Strength

Alligation Tips

•

• Solvents and diluents such as Solvents and diluents such as waterwater, vanishing cream base, and white, vanishing cream base, and white petrolatum are considered a percent strength of zero.

petrolatum are considered a percent strength of zero. •

• Liquids, including solutions, syrups, elixirs, and even lotions, areLiquids, including solutions, syrups, elixirs, and even lotions, are express

expressed in ed in milliliters.milliliters. •

• Solids are expressed in grams. This would include powders, creams,Solids are expressed in grams. This would include powders, creams, and ointments.

and ointments. •

• The alligation formula requires that you express the strength as aThe alligation formula requires that you express the strength as a percentage when setting up the problem. You would have to convert percentage when setting up the problem. You would have to convert a ratio strength given in the question to

a ratio strength given in the question to a percent strea percent strength.ngth. •

• When writing percents or using decimals, always use a leading zero: When writing percents or using decimals, always use a leading zero: 0.25%. This helps prevent errors in interpretation. It would be a 0.25%. This helps prevent errors in interpretation. It would be a ter-rible error and possibly even fatal to dispense something in 25% that rible error and possibly even fatal to dispense something in 25% that was really supposed to be 0.25%.

was really supposed to be 0.25%. •

• 1 f1 fl. ol. oz.z. 2929.5.57 m7 mL. TL. Thihis is s is cocommmmononly rly rououndnded ed to 3to 30 m0 mL.L. •

• 1 av1 avoiroirdupdupois ois oz.oz. 28.28.35 g35 g. Thi. This mes measasururemeement, unt, used sed for for solsolidsids, is, is also commonly rounded to 30 g.

also commonly rounded to 30 g. =

=

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EXAMPLE 7.1

EXAMPLE 7.1 _{Rx—Prepare 120 g of a 2%}_{Rx—Prepare 120 g of a 2% hydrocortiso}_{hydrocortisone ointment using a 1%}_{ne ointment using a 1%}

ointment and a 2.5% ointment. ointment and a 2.5% ointment.

Let’

Let’s look at s look at the information that has the information that has been provided.been provided. 2 2.5.5%% HHiigghheer r StStrreennggtthh 1 1%% LLoowweer r SSttrreennggtthh 2 2%% DDeessiirreed d SSttrreennggtthh 1 120 20 gg DeDessirired ed QuQuanantitityty

First, draw the alligation grid. First, draw the alligation grid.

Now

Now, fill , fill in the alligation in the alligation grid with the grid with the information that has been information that has been providedprovided in the problem.

in the problem. •

• The higher strength goes in the top The higher strength goes in the top left box.left box. •

• The lower strength goes in the bottom left The lower strength goes in the bottom left box.box. •

• The desired strength goes in the center box.The desired strength goes in the center box.

Higher………..2.5 Higher………..2.5 Desired……….2 Desired……….2 Lower…...……..1 Lower…...……..1 Higher………..2.5 Higher………..2.5 Desired……….2 Desired……….2 Lower…...……..1 Lower…...……..1

Next, we will calculate the numbers that should go into the top right and Next, we will calculate the numbers that should go into the top right and bottom right boxes.

bottom right boxes.

This is done by working diagonally and taking the difference between the two This is done by working diagonally and taking the difference between the two numbers already in place.

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Let’s look at the first diagonal, which contains 2.5 and 2. The difference Let’s look at the first diagonal, which contains 2.5 and 2. The difference of these two numbers will go in the bottom right box.

of these two numbers will go in the bottom right box.

2.5 2.5 2 2 1 1 2.5 2.5 2 2 1 1 0.50.5 2.5 2.5 2 2 0.5 0.5 1 1 2.5 2.5 11 2 2 0.5 0.5 1 1

The difference between 2.5 and 2 is 0.5, so 0.5 goes in the bottom The difference between 2.5 and 2 is 0.5, so 0.5 goes in the bottom right box.

right box.

2.5

2.5 -- 22 == 0.50.5

Now, we can work on the other diagonal, which contains 1 and 2. Now, we can work on the other diagonal, which contains 1 and 2. The

Thedifferedifference of these two numbnce of these two numbers will go into the top right box.ers will go into the top right box.

The differenc

The difference between 1 and 2 is e between 1 and 2 is 1, so 1 goes in 1, so 1 goes in the top right box.the top right box.

Only positive numbers can go into the alligation grid, so

Only positive numbers can go into the alligation grid, so --1 is changed1 is changed t

too 11..

1

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The numbers on the right-hand side of the alligation grid represent the The numbers on the right-hand side of the alligation grid represent the number of parts per ingredient, when read straight across. This means that number of parts per ingredient, when read straight across. This means that there should be 1 part of the 2.5% ointment and 0.5

there should be 1 part of the 2.5% ointment and 0.5 parts of the 1% ointmentparts of the 1% ointment to make the 2% ointment.

to make the 2% ointment.

2.5 2.5 2 2 1 1 1 1 00..55 2.5 2.5 2 2 1 1 1 1 00..55 1.5 1.5

Now, by adding the numbers in the right column, we can determine the Now, by adding the numbers in the right column, we can determine the total number of parts necessary. In other words,

total number of parts necessary. In other words, 1 part (2.5%)

1 part (2.5%)++ 0.5 part (1%)0.5 part (1%)==1.5 parts total1.5 parts total

Now that we have determined the number of parts needed for each Now that we have determined the number of parts needed for each ingredient and the total number of parts to be used, we can set these up as ingredient and the total number of parts to be used, we can set these up as proportions. proportions. 2.5% ointment 2.5% ointment or or 1% ointment 1% ointment or or

Finally, we can take the proportion of parts needed of each ointment and Finally, we can take the proportion of parts needed of each ointment and multiply it by the desired quantity to determine the quantity

multiply it by the desired quantity to determine the quantity of each ingredi-of each ingredi-ent needed. ent needed. 0.5 0.5 1.5 1.5 0.5 part 0.5 part 1.5 parts 1.5 parts 1 1 1.5 1.5 1 part 1 part 1.5 parts 1.5 parts parts needed parts needed total parts total parts

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2.5% ointment 2.5% ointment

1

1% ointment% ointment

So, we would combine 80 g of the 2.5% ointment and 40 g of the 1% So, we would combine 80 g of the 2.5% ointment and 40 g of the 1% ointment to produce 120 g of a 2%

ointment to produce 120 g of a 2% ointment.ointment.

EXAMPLE 7.2

EXAMPLE 7.2 Rx—Prepare 90 g of triamcinolone 0.05% cream. In stock, you Rx—Prepare 90 g of triamcinolone 0.05% cream. In stock, you havehave

454 g each of

454 g each of triamcinolone 0.025% cream and triamcinolone 0.1%triamcinolone 0.025% cream and triamcinolone 0.1% cream.

cream.

Let’s look at the information that has been provided. Let’s look at the information that has been provided.

0 0..11%% HHiigghheer Sr Sttrreennggtthh 0. 0.02025%5% LoLowewer r StStrerengngthth 0 0.0.055%% DDeessiirreed d StStrreennggtthh 9 90 0 gg DDeessiirreed d QQuuaannttiittyy

First, draw the alligation grid. First, draw the alligation grid.

120 g 120 g ** 0.50.5 1.5 1.5 == 40 g40 g 120 g 120 g ** 11 1.5 1.5 == 80 g80 g Higher………..0.1 Higher………..0.1 Desired……….0.05 Desired……….0.05 Lower…...…0.025 Lower…...…0.025 Now

Now, fill in , fill in the alligation grid with tthe alligation grid with the information that has been providedhe information that has been provided in the problem.

in the problem. •

• The higher strength goes in the top left The higher strength goes in the top left box.box. •

• The lower strength goes in the bottom left box.The lower strength goes in the bottom left box. •

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Next, we will calculate the numbers that should go into

Next, we will calculate the numbers that should go into the top right andthe top right and bottom right boxes.

bottom right boxes.

Higher………..0.1 Higher………..0.1 Desired……….0.05 Desired……….0.05 Lower…...0.025 Lower…...0.025 0.1 0.1 0.05 0.05 0.025 0.025 0.1 0.1 0.05 0.05 0.025 0.025 0.050.05

This is done by working diagonally and taking the difference between This is done by working diagonally and taking the difference between the two numbers already in

the two numbers already in place.place.

Let’s look at the first diagonal, which contains 0.1 and 0.05. The Let’s look at the first diagonal, which contains 0.1 and 0.05. The differ-ence of these two numbers will go in

ence of these two numbers will go in the bottom right box.the bottom right box.

The difference between 0.1 and 0.05 is 0.5, so 0.05 goes in the bottom The difference between 0.1 and 0.05 is 0.5, so 0.05 goes in the bottom right box.

right box.

0.1

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Now, we can work on the other diagonal, which contains 0.025 and Now, we can work on the other diagonal, which contains 0.025 and 0.05. The difference of these two numbers will go into the

0.05. The difference of these two numbers will go into the top right box.top right box.

0.1 0.1 0.05 0.05 0.025 0.025 0.050.05 0.1 0.1 0.05 0.05 0.05 0.05 0.025 0.025 0.025 0.025 0.025 0.025 0.05 0.05 0.025 0.025 0.1 0.1 0.05 0.05 The differenc

The difference between 0.025 and 0.05 is 0.025, e between 0.025 and 0.05 is 0.025, so 0.025 goes in the topso 0.025 goes in the top right box.

right box.

Remember, only positive numbers can go into the alligation grid, so Remember, only positive numbers can go into the alligation grid, so

--0.025 is changed to 0.025.0.025 is changed to 0.025. 0.025

0.025 -- 0.050.05 == __0.0250.025

The numbers on the right-hand side of the alligation grid represent the The numbers on the right-hand side of the alligation grid represent the number of parts per ingredient, when read straight across. This means that number of parts per ingredient, when read straight across. This means that there should be 0.025 part of the 0.1% cream and 0.05 part of the 0.025% there should be 0.025 part of the 0.1% cream and 0.05 part of the 0.025% cream to make the 0.05% cream.

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Now that we have determined the number of parts needed for each Now that we have determined the number of parts needed for each ingredient and the total number of parts to be used, we can set these up as ingredient and the total number of parts to be used, we can set these up as proportions. proportions. 0.1% cream 0.1% cream or or 0.025% cream 0.025% cream or or

Finally, we can take the proportion of parts needed of each cream and Finally, we can take the proportion of parts needed of each cream and multiply it by the desired quantity to determine the quantity

multiply it by the desired quantity to determine the quantity of each ingredi-of each ingredi-ent needed. ent needed. 0.1% cream 0.1% cream 0.025% cream 0.025% cream

So, we would combine 30 g of the 0.1% cream and 60 g of the 0.025% So, we would combine 30 g of the 0.1% cream and 60 g of the 0.025% cream to produce 90 g of a 0.5% cream.

cream to produce 90 g of a 0.5% cream.

EXAMPLE 7.3

EXAMPLE 7.3 _{Rx—How much of a 2.5% cream and a 0.5% cream would be}_{Rx—How much of a 2.5% cream and a 0.5% cream would be}

required to compound 100 g of a

required to compound 100 g of a 1% cream?1% cream? Let’

Let’s look at s look at the information that has the information that has been provided.been provided. 2.

2.5%5% HHigighher er StStrrenengtgthh 0.

0.5 %5 % LLowower er StStrrenengtgthh 1

1%% DDeessiirreed Sd Sttrreennggtthh 10

100 g0 g DeDesisirred ed QuQuanantitityty

90 g 90 g ** 0.050.05 0.075 0.075 == 60 g60 g 90 g 90 g ** 0.0250.025 0.075 0.075 == 30 g30 g 0.05 0.05 0.075 0.075 0.05 part 0.05 part 0.075 part 0.075 part 0.025 0.025 0.075 0.075 0.025 part 0.025 part 0.075 part 0.075 part parts needed parts needed total parts total parts 0.025 0.025 0.05 0.05 0.025 0.025 0.1 0.1 0.05 0.05 0.075 0.075

total number of parts necessary. In other words, 0.025 part (0.1%)

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Now

Now, fill in , fill in the alligation grid with tthe alligation grid with the information that has been providedhe information that has been provided in the problem.

in the problem. •

• The lower strength goes in the bottom left box.The lower strength goes in the bottom left box. •

• The desired strength goes in the The desired strength goes in the center box.center box.

Higher………..2.5 Higher………..2.5 Desired……….1 Desired……….1 Lower…...……..0.5 Lower…...……..0.5 Higher………..2.5 Higher………..2.5 Desired……….1 Desired……….1 Lower…...……..0.5 Lower…...……..0.5 2.5 2.5 1 1 0.5 0.5

Next, we will calculate the numbers that

Next, we will calculate the numbers that should go into the top right should go into the top right and bot-and bot-tom right boxes.

tom right boxes.

Let’s look at the first diagonal, which contains 2.5 and 1. The difference Let’s look at the first diagonal, which contains 2.5 and 1. The difference of these two numbers will go in the bottom right box.

of these two numbers will go in the bottom right box. First, draw the alligation grid.

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The difference between 2.5 and 1 is 1.5, so 1.5 goes in the bottom The difference between 2.5 and 1 is 1.5, so 1.5 goes in the bottom right box. right box. 2.5 2.5 -- 11 == 1.51.5 2.5 2.5 1 1 0.5 0.5 1.51.5 2.5 2.5 1 1 0 0..5 5 11..55 2.5 2.5 1 1 0 0..5 5 11..55 0.5 0.5 2.5 2.5 1 1 0 0..5 5 11..55 0.5 0.5

Now, we can work on the other diagonal, which contains 0.5 and 1. The Now, we can work on the other diagonal, which contains 0.5 and 1. The differ

difference of these two numbers will go ence of these two numbers will go into the top right into the top right box.box.

The differe

The difference between 0.5 and 1 is 0.5, so 0.5 goes in the nce between 0.5 and 1 is 0.5, so 0.5 goes in the top right box.top right box.

Remember

Remember, only , only positive numbers can go positive numbers can go into the into the alligation grid, soalligation grid, so --0.50.5

is changed to 0.5. is changed to 0.5.

0.5

0.5 -- 11 == 0.50.5

The numbers on the right-hand side of the alligation grid represent the The numbers on the right-hand side of the alligation grid represent the number of parts per ingredient, when read straight across. This means that number of parts per ingredient, when read straight across. This means that there should be 0.5 part of the 2.5% cream and 1.5 parts of the 0.5% cream to there should be 0.5 part of the 2.5% cream and 1.5 parts of the 0.5% cream to make the 1% cream.

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total number of parts necessary. In other words, 0.5 part (2.5%)

0.5 part (2.5%) ++1.5 parts (0.5%)1.5 parts (0.5%) ==2 parts total2 parts total

2.5 2.5 2 2 1 1 0.5 0.5 0.5 0.5 1.5 1.5

Now that we have determined the number of parts needed for each Now that we have determined the number of parts needed for each ingredient and the total number of parts to be used, we can set these up as ingredient and the total number of parts to be used, we can set these up as proportions. proportions. 2.5% cream 2.5% cream or or 0.5% cream 0.5% cream or or

Finally, we can take the proportion of parts needed of each cream and Finally, we can take the proportion of parts needed of each cream and multiply it by the

multiply it by the desired quantity to determine the quantity of each ingredi-desired quantity to determine the quantity of each ingredi-ent needed. ent needed. 2.5% cream 2.5% cream 0.5% cream 0.5% cream

So, we would combine 25 g of the 2.5% cream and 75 g of the 0.5% So, we would combine 25 g of the 2.5% cream and 75 g of the 0.5% cream to produce 100 g of a 1% cream.

cream to produce 100 g of a 1% cream. 100 g 100 g ** 1.51.5 2.0 2.0 == 75 g75 g 100 g 100 g ** 0.50.5 2 2 == 25 g25 g 1.5 1.5 2 2 1.5 parts 1.5 parts 2 parts 2 parts 0.5 0.5 2 2 0.5 part 0.5 part 2 parts 2 parts parts needed parts needed total parts total parts

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EXAMPLE 7.4

EXAMPLE 7.4 _{Rx—Prepare 500 mL of a 7.5%}_{Rx—Prepare 500 mL of a 7.5%}_{dextrose solution using SWFI}_{dextrose solution using SWFI}

and D10W. and D10W.

Let’

Let’s look at s look at the information that has the information that has been provided.been provided. 1 100%% HHiigghheer r SSttrreennggtthh 0 0%% LLoowweer r SSttrreennggtthh 7 7..55%% DDeessiirreed Sd Sttrreennggtthh 50

500 m0 mLL DeDesisirred Qed Quauantntitityy

D10W stands for dextrose 10% in water, thus making it a 10%

D10W stands for dextrose 10% in water, thus making it a 10% strength.strength. Don’t forget that bases, such as SWFI are 0%

Don’t forget that bases, such as SWFI are 0% strength, since they contain no ac-strength, since they contain no ac-tive ingredient.

tive ingredient.

Now

Now, fill , fill in the in the alligation grid with alligation grid with the information that the information that has been providedhas been provided in the problem.

in the problem. •

• The desired strength goes in the The desired strength goes in the center box.center box.

Higher………..10 Higher………..10 Desired……….7.5 Desired……….7.5 Lower…...0 Lower…...0 10 10 7.5 7.5 0 0

bottom right boxes.

Let’s look at the first diagonal, which contains 10 and 7.5. The difference Let’s look at the first diagonal, which contains 10 and 7.5. The difference of these two numbers will go in the bottom right box.

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The difference between 10 and 7.5 is 2.5, so 2.5 goes in the bottom The difference between 10 and 7.5 is 2.5, so 2.5 goes in the bottom right box. right box. 10 10 -- 7.57.5 == 2.52.5 10 10 7.5 7.5 0 0 2.52.5 10 10 7.5 7.5 2.5 2.5 0 0 10 10 7.5 7.5 2.5 2.5 0 0 7.5 7.5

Now, we can work on the other diagonal, which contains 0 and 7.5. The Now, we can work on the other diagonal, which contains 0 and 7.5. The differe

difference of these two numbers will go nce of these two numbers will go into the top right into the top right box.box.

The differe

The difference between 0 and 7.5 is 7.5, so 7.5 goes in the nce between 0 and 7.5 is 7.5, so 7.5 goes in the top right box.top right box.

Remember, any negative number must be changed to a positive number Remember, any negative number must be changed to a positive number to be used in the grid.

to be used in the grid.

0

0 -- 7.57.5 == __7.57.5

The numbers on the right-hand side of the alligation grid represent the The numbers on the right-hand side of the alligation grid represent the number of parts per ingredient, when read straight across. This means that number of parts per ingredient, when read straight across. This means that there should be 7.5 parts of the

there should be 7.5 parts of the D10W and 2.5 parts of the D10W and 2.5 parts of the SWFI to prepare aSWFI to prepare a 7.5% dextrose solution.

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total number of parts necessary. In other words, 7.5 parts (10%)

7.5 parts (10%)++ 2.5 parts (0%)2.5 parts (0%)==10 parts total10 parts total

7.5 7.5 7.5 7.5 0 0 10 10 2.5 2.5 7.5 7.5 7.5 7.5 0 0 10 10 2.5 2.5 10 10

Now that we have determined the number of parts needed for each Now that we have determined the number of parts needed for each ingredi-ent and the total number of parts to be used, we can set these up as proportions. ent and the total number of parts to be used, we can set these up as proportions.

D10W D10W or or SWFI SWFI or or

Finally, we can take the proportion of parts needed of each cream and Finally, we can take the proportion of parts needed of each cream and multi-ply it by the desired quantity to determine the quantity of each ingredient needed. ply it by the desired quantity to determine the quantity of each ingredient needed.

D10W D10W

SWFI SWFI

So, we would combine 375 mL of the

So, we would combine 375 mL of the D10W and 125 mL of the SWFI D10W and 125 mL of the SWFI toto prepare 500 mL of a 7.5% dextrose solution.

prepare 500 mL of a 7.5% dextrose solution. 500 mL 500 mL ** 2.52.5 10 10 == 125 mL125 mL 500 mL 500 mL ** 7.57.5 10 10 == 375 mL375 mL 2.5 2.5 10 10 2.5 parts 2.5 parts 10 parts 10 parts 7.5 7.5 10 10 7.5 parts 7.5 parts 10 parts 10 parts parts needed parts needed total parts total parts

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EXAMPLE 7.5

EXAMPLE 7.5 _{Rx—Prepare 1 L of a 20%}_{Rx—Prepare 1 L of a 20% alcohol solution using a 90% alcohol and}_{alcohol solution using a 90% alcohol and}

a 10% alcohol. a 10% alcohol.

Let’

Let’s look at s look at the information that has the information that has been provided.been provided. 9 900%% HHiigghheer r SSttrreennggtthh 1 100%% LLoowweer r SSttrreennggtthh 2 200%% DDeessiirreed d SSttrreennggtthh 1

1 L L (1(100000 0 mmL)L) DeDessirired ed QuQuanantitittyy

Now

Now, fill in , fill in the alligation grid with the the alligation grid with the information that has been providedinformation that has been provided in the

in the problem.problem. •

• The higher strength goes in the top The higher strength goes in the top left box.left box. •

• The desired strength goes in the center box.The desired strength goes in the center box.

90 90 20 20 10 10 7070

bottom right boxes.

Let’s look at the first diagonal, which contains 90 and 20. The difference Let’s look at the first diagonal, which contains 90 and 20. The difference of these two numbers will go in the bottom right box.

of these two numbers will go in the bottom right box.

Higher………..90 Higher………..90 Desired……….20 Desired……….20 Lower…...……..10 Lower…...……..10 90 90 20 20 10 10 The differenc

The difference between 90 and 20 is 70, so 70 goes in the bottom right e between 90 and 20 is 70, so 70 goes in the bottom right box.box. 90

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Now, we can work on the other diagonal, which contains 10 and 20. The Now, we can work on the other diagonal, which contains 10 and 20. The differ

difference of these two numbers will go ence of these two numbers will go into the top right into the top right box.box.

90 90 20 20 70 70 10 10 90 90 20 20 70 70 10 10 10 10 90 90 20 20 1 100 7700 10 10

The difference between 10 and 20 is 10, so 10 goes in the top right box. The difference between 10 and 20 is 10, so 10 goes in the top right box.

Remember, any negative number must be changed to a positive number Remember, any negative number must be changed to a positive number to be used in the grid.

to be used in the grid.

10

10 -- 2020 == __1010

The numbers on the right-hand side of the alligation grid represent the The numbers on the right-hand side of the alligation grid represent the number of parts per ingredient, when read straight across. This means that number of parts per ingredient, when read straight across. This means that there should be 10 parts of the

there should be 10 parts of the 90% alcohol and 70 parts of 90% alcohol and 70 parts of the 10% alcoholthe 10% alcohol to prepare a 20% alcohol solution.

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total number of parts necessary. In other words, 10 parts (90%)

10 parts (90%) ++ 70 parts (10%)70 parts (10%) ==80 parts total80 parts total

90 90 20 20 10 10 10 10 70 70 80 80

Now that we have determined the number of parts needed for each Now that we have determined the number of parts needed for each ingredient and the total number of parts to be used, we can set these up as ingredient and the total number of parts to be used, we can set these up as proportions. proportions. 90% alcohol 90% alcohol or or 10% alcohol 10% alcohol or or

Finally, we can take the proportion of parts needed of each cream and Finally, we can take the proportion of parts needed of each cream and multiply it by the

multiply it by the desired quantity to determine the quantity of each ingredi-desired quantity to determine the quantity of each ingredi-ent needed. ent needed. 90% alcohol 90% alcohol 10% alcohol 10% alcohol

So, we would combine 125 mL of the 90% alcohol and 875 mL of the So, we would combine 125 mL of the 90% alcohol and 875 mL of the 10% alcohol to prepare 1 L of a

10% alcohol to prepare 1 L of a 20% alcohol.20% alcohol. 1000 mL 1000 mL ** 7070 80 80 == 875 mL875 mL 1000 mL 1000 mL ** 1010 80 80 == 125 mL125 mL 70 70 80 80 70 parts 70 parts 80 parts 80 parts 10 10 80 80 10 parts 10 parts 80 parts 80 parts parts needed parts needed total parts total parts

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PRACTICE PROBLEMS 7.1 PRACTICE PROBLEMS 7.1 Calculate the following alligations. Calculate the following alligations.

1

1.. Rx silver nitrate 0.25% solution 1 LRx silver nitrate 0.25% solution 1 L Y

You have a gallon of ou have a gallon of silver nitrate 1% stock solution, which you willsilver nitrate 1% stock solution, which you will dilute with distilled water. How many milliliters of

dilute with distilled water. How many milliliters of each will you needeach will you need to make the final product? Note that the percent strength of water is to make the final product? Note that the percent strength of water is zero. ________________ ________________

zero. ________________ ________________ 2

2.. Rx soaking solution 1:100 1 LRx soaking solution 1:100 1 L

You have a 1:25 stock solution and water. How many milliliters of each You have a 1:25 stock solution and water. How many milliliters of each will you need to make the final

will you need to make the final product? ________________product? ________________ ________________

________________ 3

3.. Rx coal tar 5% ointment 120 gRx coal tar 5% ointment 120 g

You have coal tar 10% ointment and coal tar 2% ointment. How many You have coal tar 10% ointment and coal tar 2% ointment. How many grams of each will you use to prepare the final product?

grams of each will you use to prepare the final product? ________________

________________ 4

4.. You are instructed to prepare 454 g of a 15% ointment. In stock youYou are instructed to prepare 454 g of a 15% ointment. In stock you have 5% and 30%. How much of each will

have 5% and 30%. How much of each will you need to use to you need to use to make themake the order? ________________

order? ________________ 5

5.. Rx—PrepaRx—Prepare 480 mL of a 1:30 re 480 mL of a 1:30 solution using a 1:10 solution and solution using a 1:10 solution and a 1:50a 1:50 solution.

solution.

What quantities will be used of each stock solution to

What quantities will be used of each stock solution to make the 1:30make the 1:30 solution? ________________

solution? ________________ 6

6.. You need to prepare 80 g of a 9% cream using a 20% stock cream and aYou need to prepare 80 g of a 9% cream using a 20% stock cream and a cream base. How much are needed of each? ________________

cream base. How much are needed of each? ________________ 7

7.. You are asked to prepare 1 L of a 1:300 soaking solution, using a stockYou are asked to prepare 1 L of a 1:300 soaking solution, using a stock 1:500 soaking solution and

1:500 soaking solution and distilled waterdistilled water. How much . How much of each will youof each will you need to use? ________________

need to use? ________________ 8

8.. How much SWFI would need to be added to 500 How much SWFI would need to be added to 500 mL stock normalmL stock normal saline (0.9% NaCL) to produce a 0.45% sodium chloride solution? saline (0.9% NaCL) to produce a 0.45% sodium chloride solution? ________________

________________ 9

9.. Rx alcohol 30%Rx alcohol 30%

How many milliliters of 90% alcohol should you add to

How many milliliters of 90% alcohol should you add to 25 mL of 10%25 mL of 10% alcohol to make 30% alcohol? ________________

alcohol to make 30% alcohol? ________________ 1

10.0. Rx hydrocortisone 2% ointmentRx hydrocortisone 2% ointment

How many grams of petrolatum should you add to 30 g of How many grams of petrolatum should you add to 30 g of hydrocor

hydrocortisone 2.5% ointment to tisone 2.5% ointment to reduce its strength to 2.0%? Thereduce its strength to 2.0%? The perc

percent strength of petrolatum is zero. _______ent strength of petrolatum is zero. _________________________ 1

11.1. Rx normal salineRx normal saline

How many milliliters of water must you add to

How many milliliters of water must you add to 500 mL of a 10% 500 mL of a 10% stockstock solution of sodium chloride to make a batch of

solution of sodium chloride to make a batch of normal saline (sodiumnormal saline (sodium chloride 0.9% solution)? ________________

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12

12.. Rx ichthammol 5% ointmentRx ichthammol 5% ointment

How many grams of ichthammol 10% ointment should you add to 20 How many grams of ichthammol 10% ointment should you add to 20 gg of ichthammol 2% ointment to make ichthammol 5% ointment?

of ichthammol 2% ointment to make ichthammol 5% ointment? ________________

________________ 13

13.. Rx benzalkonium chloride 1:1000 solutionRx benzalkonium chloride 1:1000 solution

How many milliliters of water should you add to 50

How many milliliters of water should you add to 50 mL of mL of benzalkonium chloride 0.25% solution to prepare the order? benzalkonium chloride 0.25% solution to prepare the order? ________________

________________ 14

14.. Rx zinc oxide 10% ointment 45 gRx zinc oxide 10% ointment 45 g

How many grams of zinc oxide 20% ointment and zinc oxide 5% How many grams of zinc oxide 20% ointment and zinc oxide 5% ointment should you mix to prepare the order? ________________ ointment should you mix to prepare the order? ________________ ________________

________________ 15

15.. Rx aluminum acetate 1:400 solution 1 gallonRx aluminum acetate 1:400 solution 1 gallon

How many milliliters of Burrow’s solution (aluminum acetate 5%) How many milliliters of Burrow’s solution (aluminum acetate 5%) should you use to prepare the order? ________________

should you use to prepare the order? ________________ 16

16.. Rx histamine phosphate 1:10,000 solution 10 mLRx histamine phosphate 1:10,000 solution 10 mL

How many milliliters of a histamine phosphate 1:10 solution do you How many milliliters of a histamine phosphate 1:10 solution do you need to prepare the order? ________________

need to prepare the order? ________________ 17

17.. Rx benzocaine 5% ointment 2 oz.Rx benzocaine 5% ointment 2 oz.

How many grams of benzocaine 2% ointment should you mix with 22.5 g How many grams of benzocaine 2% ointment should you mix with 22.5 g of benzocaine 10% ointment to

of benzocaine 10% ointment to preparprepare the order? ________________e the order? ________________ 18

18.. When using a 0.5% cream and a 2% cream to produce a 1.25% cream, When using a 0.5% cream and a 2% cream to produce a 1.25% cream, how many p

how many parts of eaarts of each are nech are needed?eded?________________________________ 19

19.. In what proportion would you add SWFI with D10W to produce D6W?In what proportion would you add SWFI with D10W to produce D6W? ________________

________________ 20

20.. In what proportion should you add a 1:20 soaking solution withIn what proportion should you add a 1:20 soaking solution with distilled wate

distilled water to crear to create a 1:50 solution?te a 1:50 solution?________________________________

SUMMARY

In certain situations, a pharmacy must use the alligation method to combine In certain situations, a pharmacy must use the alligation method to combine two varying strengths of a drug or combine a drug with a base or diluent to two varying strengths of a drug or combine a drug with a base or diluent to achieve the prescribed strength. While these calculations can be

achieve the prescribed strength. While these calculations can be confusing atconfusing at first, once you master the alligation grid you

first, once you master the alligation grid you should be able to perform theseshould be able to perform these calculations easily.

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CHAPTER REVIEW QUESTIONS

CHAPTER

7

MUL

MULTIPLE TIPLE CHOICECHOICE 1

1.. How much 20How much 20% cream % cream should you adshould you add to 26d to 26gg of 1% cream to make a 4% cream?

of 1% cream to make a 4% cream? ________________ ________________ a. a. 6.00 g6.00 g c.c. 4.88 g4.88 g b. b. 5.20 g5.20 g d.d.3.00 g3.00 g 2

2.. How much 25% stock solution and distilledHow much 25% stock solution and distilled water will yo

water will you need to mau need to make 1ke 1 L of aL of a solution? ________________

solution? ________________ a.

a. 1010mL of tmL of the 25he 25% sol% solutioution and 9n and 99090mLmL of water

of water b.

b. 100100mL of thmL of the 25% se 25% solutolution anion and 900d 900mLmL of water

of water c.

c. 990990mL of thmL of the 25% se 25% solutolution anion and 10d 10mLmL of water

of water d.

d.900900mL of thmL of the 25% se 25% solutolution anion and 10d 10mLmL of water

of water 3

3.. How much 10% cream and a 0.5% cream willHow much 10% cream and a 0.5% cream will you need to pre

you need to prepare 120pare 120g of a 2.5% creag of a 2.5% cream?m? ________________

________________ a.

a. 20 g of the 10% cream and 20 g of the 10% cream and 100 g of the 0.5%100 g of the 0.5% cream

cream b.

b. 100 g of the 10% cream and 20 100 g of the 10% cream and 20 g of the 0.5%g of the 0.5% cream

cream c.

c. 25 g of the 10% cream and 25 g of the 10% cream and 95 g of the 0.5%95 g of the 0.5% cream

cream d.

d.95 g of the 10% cream and 95 g of the 10% cream and 25 g of the 0.5%25 g of the 0.5% cream

cream

1 1::400400

4.

4. How much povidone iodine 20% solution andHow much povidone iodine 20% solution and water will y

water will you need to mou need to make 500ake 500mL of amL of a povidone iodine 3% rinse? ________________ povidone iodine 3% rinse? ________________ ________________

________________ a.

a. 7575mL of thmL of the 20% se 20% solutiolution and 4on and 42525mL of wmL of waterater b.

b. 425425mL of mL of the 2the 20% so0% solution lution and 25and 25mL omL of f water

water c.

c. 2020mL of thmL of the 20% se 20% soluolution ation and 480nd 480mL of mL of water

water d.

d. 480480mL of mL of the 2the 20% so0% solution lution and 20and 20mL omL of f water

water 5.

5. How much lidocaine 0.5% topical gel shouldHow much lidocaine 0.5% topical gel should you mix with lidocaine 10% topical gel to you mix with lidocaine 10% topical gel to makemake 15

15 g of a g of a lidocaine 2lidocaine 2% topical % topical gel?gel? ________________ ________________ a. a. 2.4 g2.4 g c.c. 9.5 g9.5 g b. b. 5.0 g5.0 g d.d.12.6 g12.6 g 6.

6. How How much much solution solution and and solutionsolution should

should you you mix mix to to make make 11 L L of of a a soakingsoaking solution? ________________

solution? ________________ a.

a. 947947mL mL of of the the solutiosolution n and and 5353mL mL of of thethe solution

solution b.

b. 5353mL mL of of the the solsolutioution n and and 947947mL mL of of thethe solution

solution c.

c. 250250mL mL of of the the solutiosolution n and and 750 750 of of thethe solution

solution d.

d. 750750mL mL of of the the solutiosolution n and and 250250mL mL of of the solution the 11::500500 solution 1 1::2525 1 1::500500 1 1::2525 1 1::500500 1 1::2525 1 1::500500 1 1::2525 1 1::250250 1 1::500500 1 1::2525

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7

7.. Convert 50% to a ratio strength.Convert 50% to a ratio strength. ________________ ________________ a a.. cc.. b b.. dd.. 8

8.. How much NaCl 10% stock solution shouldHow much NaCl 10% stock solution should you add to

you add to 100100mL of NaCl 0mL of NaCl 0.45% solution to.45% solution to make normal saline? ________________ make normal saline? ________________ a.

a. 11mLmL c.c. 55 mLmL b.

b. 22mLmL d.d.1100 mmLL 9

9.. How many grams of 0.1% cream should youHow many grams of 0.1% cream should you mix with 12

mix with 12g of 12% crg of 12% cream to maeam to make a 6%ke a 6% cream? ________________ cream? ________________ a. a. 10.4 g10.4 g c.c. 24 g24 g b. b. 12.2 g12.2 g d.d.33 g33 g 10

10.. How many parts of each of a 1% product and aHow many parts of each of a 1% product and a 3% product do you need to make a 2.5% product? 3% product do you need to make a 2.5% product? ______

__________________________________________________________ a.

a. 2.5 parts of the 1% product and 1 part of the2.5 parts of the 1% product and 1 part of the 3% product

3% product b.

b. 1 part of the 1% product and 2.5 parts of the1 part of the 1% product and 2.5 parts of the 3% product

3% product c.

c. 1.5 parts of the 1% product and 0.5 part of 1.5 parts of the 1% product and 0.5 part of the 3% product

the 3% product d.

d. 0.5 part of the 1% product and 1.5 parts of 0.5 part of the 1% product and 1.5 parts of the 3% product

the 3% product

TRUE OR FALSE TRUE OR FALSE 11

11.. When using the alligation method, you must When using the alligation method, you must consider three different percent strengths: the consider three different percent strengths: the beginning strength of each ingredient and beginning strength of each ingredient and the final strength. ________________ the final strength. ________________ a.

a. truetrue b.b. falsefalse 12

12.. When using the alligation method, the final When using the alligation method, the final strength will be a value between the beginning strength will be a value between the beginning two strengths. ________________

two strengths. ________________ a.

a. truetrue b.b. falsefalse 1 1::88 1 1::44 1 1::66 1 1::22 1

13.3. Distilled water, with a percent strength of zero,Distilled water, with a percent strength of zero, is sometimes used as a

is sometimes used as a beginning ingredient inbeginning ingredient in alligation problems. ________________

alligation problems. ________________ a.

14.4. When setting up an alligation, you should When setting up an alligation, you should convert any ratio strengths given to percent convert any ratio strengths given to percent strengths before setting up the formula. strengths before setting up the formula. ________________

________________ a.

15.5. Amounts needed of powders, creams, andAmounts needed of powders, creams, and ointments are expressed in milligrams. ointments are expressed in milligrams. ________________

________________ a.

a. truetrue b.b. falsefalse

SHORT ANSWER SHORT ANSWER 1

16.6. Describe the principle of alligations.Describe the principle of alligations.

_______________________________________ _______________________________________ 1

17.7. List three tips for List three tips for performing alligations.performing alligations.

_______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ 1

18.8. Describe how to verify your answer whenDescribe how to verify your answer when solving alligations.

solving alligations.

_______________________________________ _______________________________________ 1

19.9. Describe how to convert a ratio strength to aDescribe how to convert a ratio strength to a percent strength.

percent strength.

_______________________________________ _______________________________________ 2

20.0. Describe how to convert a Describe how to convert a percpercent strength to aent strength to a ratio strength.

ratio strength.

_______________________________________ _______________________________________