Jorge wants to save money for his daughter’s college education. If Jorge needs to have $4340 at the end of 4 years, how much money would he need to in- vest at a 6% simple interest rate?
Solution: Step 1: Read the problem.
Let P represent the original amount invested. Step 2: Label the variables.
Step 3: Write an equation in words.
Recall that interest is computed by the formula
Step 4: Write a mathematical equation.
Step 5: Solve the equation.
P 3500 1.24P 1.24 4340 1.24 1.24P 4340 0.24P 4340 P P10.062142 4340 P 1total2 1Prt2 1P2 I Prt. 1interest2 1total2 aprincipalboriginal Example 5 Skill Practice $12,000 $3600 $15,600 I $3600 I 1$12,000210.0752142 Example 4
Skill Practice Answers
Study Skills Exercises
1. Go to the online service called MathZone that accompanies this text (www.mathzone.com). Name two features that this online service offers that can help you in this course.
2. Define the key terms:
a. sales tax b. simple interest
Review Exercises
3. List the six steps to solve an application.
For Exercises 4–5, use the steps for problem solving to solve these applications.
4. Find two consecutive integers such that 3 times the larger is the same as 45 more than the smaller. Find
the numbers.
5. The height of the Great Pyramid of Giza is 17 m more than twice the height of the pyramid found in
Saqqara. If the difference in their heights is 77 m, find the height of each pyramid.
Concept 1: Solving Basic Percent Equations
For Exercises 6–17, find the missing values.
6. 45 is what percent of 360? 7. 338 is what percent of 520?
8. 544 is what percent of 640? 9. 576 is what percent of 800?
10. What is 0.5% of 150? 11. What is 9.5% of 616?
12. What is 142% of 740? 13. What is 156% of 280?
14. 177 is 20% of what number? 15. 126 is 15% of what number?
16. 275 is 12.5% of what number? 17. 594 is 45% of what number?
The original investment should be $3500. Step 6: Interpret the results
and write the answer in words.
7. Cassandra invested some money in her bank account, and after 10 years at
4% simple interest, it has grown to $7700. What was the initial amount invested?
Skill Practice
Skill Practice Answers
7. The initial investment was $5500.
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• Practice Problems • e-Professors • Self-Tests • Videos • NetTutor
For Exercises 18–21, use the graph showing the distribution for leading forms of cancer in men. (Source: Centers for Disease Control)
18. If there are 700,000 cases of cancer in men in the United States,
approximately how many are prostate cancer?
19. Approximately how many cases of lung cancer would be
expected in 700,000 cancer cases among men in the United States.
20. There were 14,000 cases of cancer of the pancreas diagnosed out of
700,000 cancer cases. What percent is this?
21. There were 21,000 cases of leukemia diagnosed out of 700,000 cancer cases. What percent is this? 22. A Pioneer car CD/MP3 player costs $170. Circuit City has it on sale for 12% off with free installation.
a. What is the discount on the CD/MP3 player? b. What is the sale price?
23. A laptop computer, originally selling for $899.00, is on sale for 10% off. a. What is the discount on the laptop?
b. What is the sale price?
24. A Sony digital camera is on sale for $400.00. This price is 15% off the original price. What was the original
price? Round to the nearest cent.
25. The Star Wars III DVD is on sale for $18. If this represents an 18% sale price, what was the original price
of the DVD?
26. The original price of an Audio Jukebox was $250. It is on sale for $220. What percent discount does this
represent?
27. During the holiday season, the Xbox 360 sold for $425.00 in stores. This product was in such demand that
it sold for $800 online. What percent markup does this represent? (Round to the nearest whole percent.)
Concept 2: Applications Involving Sales Tax
For Exercises 28–37, solve for the unknown quantity.
28. A Craftsman drill is on sale for $99.99. If the sales tax rate is 7%, how much will Molly have to pay for the
drill?
29. Patrick purchased four new tires that were regularly priced at $94.99 each, but are on sale for $20 off per
tire. If the sales tax rate is 6%, how much will be charged to Patrick’s VISA card?
30. The sales tax for a screwdriver set came to $1.04. If the sales tax rate is 6.5%, what was the price of the
screwdriver?
31. The sales tax for a picture frame came to $1.32. If the sales tax rate is 5.5%, what was the price of the
picture frame?
32. Sun Lei bought a laptop computer over the Internet for $1800. The total cost, including tax, came to $1890.
What is the sales tax rate?
Percent of Cancer Cases by Type (Men)
Bladder 6% Lung 13% Colon 11% All other sites
33%
Melanoma 4%
Prostate 33%
33. Jamie purchased a compact disc and paid $18.26. If the disc price is $16.99, what is the sales tax rate
(round to the nearest tenth of a percent)?
34. When the Hendersons went to dinner, their total bill, including tax, was $43.74. If the sales tax rate is 8%,
what was the original price of the dinner?
35. The admission to Walt Disney World costs $74.37 including taxes of 11%. What is the original price of a ticket?
36. A hotel room rented for five nights costs $706.25 including 13% in taxes. Find the original price of the
room rental for the five nights. Then find the price per night.
37. The price of four CDs is $74.88, including a 4% sales tax. Find the original cost of a single CD assuming all
CDs are the same price.
Concept 3: Applications Involving Simple Interest
For Exercises 38–47, solve these equations involving simple interest.
38. How much interest will Pam earn in 4 years if she invests $3000 in an account that pays 3.5% simple interest? 39. How much interest will Roxanne have to pay if she borrows $2000 for 2 years at a simple interest
rate of 4%?
40. Bob borrowed some money for 1 year at 5% simple interest. If he had to pay back a total of $1260, how
much did he originally borrow?
41. Mike borrowed some money for 2 years at 6% simple interest. If he had to pay back a total of $3640, how
much did he originally borrow?
42. If $1500 grows to $1950 after 5 years, find the simple interest rate. 43. If $9000 grows to $10,440 in 2 years, find the simple interest rate.
44. A new bank offered simple interest loans at 11% for new customers. If a customer took out a loan for
$2000 to be paid back in 18 months find
a. the interest on the loan
b. the total amount that the customer owes (principal interest).
45. Rafael has $3000 saved for a future trip to Europe. If he invests in an account that pays 4% simple interest,
how much will he have after years?
46. Perry is planning a vacation to Europe in 2 years. How much should he invest in a certificate of deposit
that pays 3% simple interest to get the $3500 that he needs for the trip? Round to the nearest dollar.
47. Sherica invested in a mutual fund and at the end of 20 years she has $14,300 in her account. If the mutual
fund returned an average yield of 8%, how much did she originally invest?
Expanding Your Skills
Percents are often used to represent rates. For example, salespeople may receive all or part of their salary as a percentage of their sales. This is called a commission. The commission rate is the percent of the sales that the salesperson receives in income.
commission 1commission rate2 1$ in merchandise sold2 212
118 12
3 2 years2,
a 5 ft
c ? b 7 ft
If the perimeter is 20 ft, then
c P a b 20 ft 5 ft 7 ft 8 ft Figure 2-9 a 5 ft c 8 ft b 7 ft P a b c 5 ft 7 ft 8 ft 20 ft Figure 2-8
In this section, we will learn how to rewrite formulas to solve for a different variable within the formula. Suppose, for example, that the perimeter of a trian- gle is known and two of the sides are known (say, sides a and b). Then the third side, c, can be found by subtracting the lengths of the known sides from the perime- ter (Figure 2-9).
1. Formulas
Literal equations are equations that contain several variables. A formula is a lit-
eral equation with a specific application. For example, the perimeter of a triangle (distance around the triangle) can be found by the formula where
a, b, and c are the lengths of the sides (Figure 2-8).
P a b c,
48. The local car dealership pays its sales personnel a commission of 25% of the dealer profit on each car sold.
The dealer made a profit of $18,250 on the cars Joëlle sold last month. What was her commission last month?
49. Dan sold a beachfront home for $650,000. If his commission rate is 4%,
what did he earn on the sale of that home?
50. A salesperson at You Bought It discount store earns 3% commission on all
appliances that he sells. If Geoff’s commission for the month was $116.37, how much did he sell?
51. Anna makes a commission at an appliance store. In addition to her base
salary, she earns a 2.5% commission on her sales. If Anna’s commission for a month was $260, how much did she sell?
52. For selling software, Tom received a bonus commission based on sales over $500. If he received $180 in
commission for selling a total of $2300 worth of software, what is his commission rate?
53. In addition to an hourly salary, Jessica earns a commission for selling ice cream bars at the beach. If she
sells $708 worth of ice cream and receives a commission of $56.64, what is her commission rate?
54. Diane sells women’s sportswear at a department store. She earns a regular salary and, as a bonus, she
receives a commission of 4% on all sales over $200. If Diane earned an extra $25.80 last week in commission, how much merchandise did she sell over $200?