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writing and solving equations

Students will be able to write and solve an equation with variables on

both sides from a description and real-world situations.

©Maneuvering the Middle LLC, 2016

Round Table

8.8A Write one‐variable equations or inequalities with variables on both sides that represent problems using rational number

coefficients and constants.

8.8C Model and solve one‐variable equations with variables on both sides of the equal sign that represent mathematical and real‐world problems using rational number coefficients and constants.

8.EE.7.B Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Ideas for Implementation: This is a great activity that allows students to work in groups, yet think independently and with structure. It also keeps students

accountable as everyone is needed to complete the activity.

*This activity is formatted to be printed double-sided. Blank pages are intentional. Directions:

1. Place students in groups of 3. Determine who is letter A,B, and C within the group.

2. Each person should get the page that corresponds to their letter (see top left corner of handout).

3. Determine the amount of time for each step (usually 1 to 3 minutes). 4. Each person works on step 1, and when time is up they pass their paper

clockwise.

5. Time is started again. Students will check the previous step and then work the next step on the page. This process continues until the problem is complete. 6. Students should then flip the page and repeat the same process on the back.

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1. Determine who will be person A, B, and C. List this below. 2. Solve ONLY one step, then pass your paper clockwise.

3. Be sure to check the prior step and initial in the box before working your own step! 4. Continue until you get your original paper back.

Unit: Linear Equations Round Table – A

Writing and solving equations : round table

Step 1:

Write an equation that can be used to represent the situation above:

Equation:___________________________________ Person from Step 2, check and initial 

Step 2:

First, check the work in Step #1 and initial in the box. Next, solve the equation, and show your work:

x = _______ Person from Step 3, check and initial 

Step 3:

First, check the work in Step #2 and initial in the box. Next, prove the solution by plugging it into both sides of the equation. Show your work:

Person from Step 1, check and initial 

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

A skier can chose between buying a season pass or paying to ski

daily. A daily pass costs $47.50 per day and includes ski rentals. A

season ski pass costs a one time fee of $390 and a daily fee of

$17.50 for ski rentals. How many days would the skier have to go

skiing in order for both options to cost the same amount?

Date _____________________________Pd______

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

19 less than a number is the same as the sum of half the number

and six. What is the number?

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Unit: Linear Equations Round Table – B

Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

On Thursday morning a bakery owner prepared by baking several pies and decorating cupcakes. She spent 90 minutes baking the pies and an average of

1.2 minutes decorating each cupcake. On Friday, she spent 58 minutes baking pies, and decorated the same number of cupcakes at an average of 1.7 minutes

per cupcake. If she spent the same total amount of time preparing on Thursday as she did on Friday, how many cupcakes did she decorate each day?

Date _____________________________Pd______

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

A sailboat rental company charges customers a fee of $78.75 plus $80.25 per hour to rent a sailboat. A second rental company charges customers a fee of $40 plus $95.75 per hour to rent a sailboat. How many hours would a customer

have to rent a sailboat in order for both companies to charge the same total amount?

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Unit: Linear Equations Round Table – C

Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

The two figures below have the same perimeter. What is the value of x?

Date _____________________________Pd______

4x

5.5x + 3

8.5x – 2

3.25x + 1

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

Nikki has 186 yards of fabric in her supply room and uses 53₄ yards of fabric per day making products for her shop. Jamie has 95 yards of fabric in her supply room and uses 2₂1 yards of fabric per day making products. If neither of

the girls buys more fabric, how many days will it take until they have the same number of remaining yards of fabric in their supply rooms?

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Name _____________________________________ Date _____________________________Pd______

Unit: Linear Equations Round Table - A

Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

A skier can chose between buying a season pass or paying to ski

daily. A daily pass costs $47.50 per day and includes ski rentals. A

season ski pass costs a one time fee of $390 and a daily fee of

$17.50 for ski rentals. How many days would the skier have to go

skiing in order for both options to cost the same amount?

47.50x = 390 + 17.50x

13 47.50x = 390 + 17.50x

47.50(13) = 390 + 17.50(13)

617.50 = 617.50

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

19 less than a number is the same as the sum of half the number

and six. What is the number?

(Answer Key)

x – 19 =

₂

1 x + 6

50 x – 19 =

₂

1 x + 6

50 – 19 =

₂

1 (50) + 6

31 = 31

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

On Thursday morning a bakery owner prepared by baking several pies and decorating cupcakes. She spent 90 minutes baking the pies and an average of

1.2 minutes decorating each cupcake. On Friday, she spent 58 minutes baking pies and decorated the same number of cupcakes at an average of 1.7 minutes per cupcake. If she spent the same total amount of time preparing on Thursday

as she did on Friday, how many cupcakes did she decorate each day?

Name _____________________________________ Date _____________________________Pd______

90 + 1.2x = 58 + 1.7x

64 90 + 1.2x = 58 + 1.7x

90 + 1.2(64) = 58 + 1.7(64)

166.8 = 166.8

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

A sailboat rental company charges customers a fee of $78.75 plus $80.25 per hour to rent a sailboat. A second rental company charges customers a fee of $40 plus $95.75 per hour to rent a sailboat. How many hours would a customer

have to rent a sailboat in order for both companies to charge the same total amount?

78.75 + 80.25x = 40 + 95.75x

2.5 78.75 + 80.25x = 40 + 95.75x

78.75 + 80.25(2.5) = 40 + 95.75(2.5)

279.38 = 279.38

(Answer Key)

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

The two figures below have the same perimeter. What is the value of x?

Name _____________________________________ Date _____________________________Pd______ 4x 4x 5.5x + 3 8.5x – 2 3.25x + 1

23.5x – 2 = 13.5x + 3

0.5 23.5x – 2 = 13.5x + 3

23.5(0.5) – 2 = 13.5(0.5) + 3

9.75 = 9.75

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Step 1:

Step 2:

Step 3:

A:

_________________________________

B:

_________________________________

C:

_________________________________

Situation:

Nikki has 186 yards of fabric in her supply room and uses 53₄ yards of fabric per day making products for her shop. Jamie has 95 yards of fabric in her supply room and uses 2₂1 yards of fabric per day making products. If neither of

the girls buys more fabric, how many days will it take until they have the same number of remaining yards of fabric in their supply rooms?