Lesson 7.1 Assignment
Name_________________________________________________________ Date__________________________
Picture This
Picture Algebra
1. The Sharks Aquatic Club recently held a fundraiser to raise money for a local charity. The
swimmers received money for each lap that they swam during a one-week period. The three
swimmers who raised the most money were Rita, John, and Rodell. Together they swam a total of
2125 laps. John swam three times as many laps as Rita, and Rodell swam 25 more laps than John.
How many laps did each swimmer swim?
a.Draw a picture to represent the situation. Label the unknown parts with variables and the
known parts with their values.
Rita: L
John:
L
L
L
Rodell:
L
L
L 25
}
2125
b. Determine the number of laps each person swam using the picture you created.
Explain your reasoning.
Laps swum by Rita: 300
Laps swum by John: 900
Laps swum by Rodell: 925
Using the picture I drew, I knew that John swam 3 times the number of laps that Rita swam.
Rodell swam 25 more laps than John, so he swam 3 times the number of laps as Rita plus
an additional 25 laps. Once I calculated how many laps Rita swam, I was able to multiply
© 2011 Carnegie Learning
that amount by 3 to get the number of laps that John swam, then add 25 to John’s amount
to get the number of laps Rodell swam.
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Lesson 7.1 Assignment
page 2
c. Write an expression for the number of laps each person swam. Let L represent the number of
laps swum by Rita.
The number of laps swum by Rita: L
The number of laps swum by John: 3L
The number of laps swum by Rodell: 3L 1 25
d. Write an equation to represent this situation.
L 1 3L 1 3L 1 25 5 2125
e. If the swimmers received $2 for every lap they swam, how much did each swimmer
earn for charity?
Rita earned $2 3 300, or $600. John earned $2 3 900, or $1800. Rodell earned $2 3 925,
© 2011 Carnegie Learning
or $1850.
122 • Chapter 7 Assignments
Lesson 7.2 Assignment
Name_________________________________________________________ Date__________________________
Maintaining a Balance
Solving Equations
1. Madison Middle School has a Math and Science Club that holds meetings after school. The club
has decided to enter a two-day competition that involves different math and science challenges.
The first day of competition involves solving multi-step math problems. Teams will receive one
point for every problem they get correct. Halfway through the day, the Madison Middle School
Team has 4 points. After a dinner break, the team does more problems and is able to finish
the day with 11 points.
a. The representation shows a balance for this situation. The left side of the balance represents
the 4 points the team had at midday plus the additional points they got after dinner.
The right side of the balance represents the total points they had at the end of the day.
What will balance 1 rectangle in this representation? Describe your strategy.
© 2011 Carnegie Learning
Strategy:
I subtracted 4 squares from each side.
What will balance 1 rectangle?
Seven squares will balance 1 rectangle.
How many problems did they get correct after dinner?
The team got 7 problems correct.
b. Rewrite the representation from part (a) using symbols. Let
5 x and
5 1 point.
Then describe how the strategies you used to determine what balanced 1 rectangle can
apply to the equation.
x 1 4 5 11
I can subtract 4 from each side.
x 1 4 2 4 5 11 2 4
x57
Chapter 7 Assignments • 123
Lesson 7.2 Assignment
page 2
c. Does the value of x maintain balance in the original equation? Substitute the value of x back
into the original equation to check. Show your work.
x 1 4 5 11
7 1 4 5 11
11 5 11
Yes. x 5 7 maintains balance in the original equation.
d. What does the value x 5 7 mean in the original situation?
The value x 5 7 is the number of additional problems the team got correct after dinner
on the first day of competition.
2. The second day of a math and science competition involves all hands-on science problems.
Because of the complexity of the problems, each team will get 3 points for every science problem
that they get correct. The Madison Middle School team is starting the day with 11 points. By the
end of the day the team had 23 points.
a. The representation shows a balance for this situation. The left side of the balance represents
the 11 points the team had at the start of the day plus the additional points they got from the
science competition. The right side of the balance represents the total points they had at
the end of the second day. What will balance 1 rectangle in this representation? Describe
Strategy:
I subtracted 11 squares from each side which left 3 rectangles on the left side and 12 squares on the right side. Then, I divided the 12 squares into 3 equal groups of 4.
124 • Chapter 7 Assignments
© 2011 Carnegie Learning
your strategy.
Lesson 7.2 Assignment
page 3
Name_________________________________________________________ Date__________________________
What will balance 1 rectangle?
Four squares will balance 1 rectangle.
How many science problems did they get correct?
They got 4 science problems correct.
b. Rewrite the representation from part (a) using symbols. Let
5 x and
5 1 point.
3x 1 11 5 23
c. Solve the equation from part (b). Write a sentence to describe how to apply inverse operations
to solve the equation. Then, solve the equation.
I will subtract 11 from each side. Then, I will divide each side by 3.
3x 1 11 5 23
3x 1 11 2 11 5 23 2 11
3x 5 12
3x ​ 5 ​ 
12 ​ 
  ___
​ ___
3
3
x 5 4
© 2011 Carnegie Learning
Chapter 7 Assignments • 125
Lesson 7.2 Assignment
page 4
d. Does the value of x that you got as your solution maintain balance in the original
equation? Substitute the value of x back into the original equation to check. Show
your work.
3x 1 11 5 23
3(4) 1 11 5 23
12 1 11 5 23
23 5 23
Yes. The value of 4 maintains balance in the equation. Therefore, the team answered © 2011 Carnegie Learning
4 science problems correctly.
126 • Chapter 7 Assignments
Lesson 7.3 Assignment
Name_________________________________________________________ Date__________________________
Planning a Graduation Party
Solving Two-Step Equations
1. Employees at Driscoll’s Electronics earn a base salary plus a 20% commission on their total sales
for the year. The employees’ base salaries differ depending on how long they have been employed.
The owner of Driscoll’s gets a report each year that shows the amount each employee who has
been there for more than one year earned.
a. Complete the table.
Employee
Base Salary
(dollars)
Amount of Sales
(dollars)
Total Salary
(dollars)
Jones
30,000
75,000
45,000
Padilla
35,000
95,000
54,000
Stewart
37,000
105,000
58,000
Freese
42,000
90,000
60,000
Gross
45,000
150,000
75,000
Lin
41,000
180,000
77,000
b. Write an equation to represent this situation. Define your variables.
© 2011 Carnegie Learning
Let b represent the base salary, s represent the amount of sales, and t represent the total
salary for each employee.
b 1 0.20s 5 t
Chapter 7 Assignments • 127
Lesson 7.3 Assignment
page 2
c. The owner decides to give everyone a raise on their base salary. Stewart’s base salary
increases to $40,000. How much must he make in sales if he wants his total salary to be
$65,000? Use your equation and write a sentence to describe how to apply inverse
operations to solve it.
I will first subtract 40,000 from each side, and then divide by 0.20.
40,000 1 0.20s 5 65,000
40,000 1 0.20s 2 40,000 5 65,000 2 40,000
0.20s 5 25,000
25,000
0.20s ​ 5 ​ 
  _______
 
 ​ 
​ ______
0.20
0.20
s 5 125,000
Stewart will need to make $125,000 in sales to have a salary of $65,000.
I can verify my solution by substituting 125,000 in the equation.
40,000 1 0.20(125,000) 5 65,000
40,000 1 25,000 5 65,000
65,000 5 65,000
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© 2011 Carnegie Learning
d. Verify your solution. Explain your reasoning.
Lesson 7.3 Assignment
page 3
Name_________________________________________________________ Date__________________________
e.The owner also gets a report on the salaries made by new employees. Each new employee gets
a base salary of $20,000 and 10% commission on their total yearly sales. Write an equation to
represent the total salary for new employees.
20,000 1 0.10s 5 t
f. Hodges, a new employee, had a total salary of $30,000 for the year. Use the equation to
determine how much he made in sales. Write a sentence to describe how to apply inverse
© 2011 Carnegie Learning
operations to solve it. Verify your solution.
I will first subtract 20,000 from each side, and then divide by 0.10.
20,000 1 0.10s 5 30,000
20,000 1 0.10s 2 20,000 5 30,000 2 20,000
0.10s 5 10,000
10,000
0.10s ​ 5 ​ 
  _______
 
 ​ 
​ ______
0.10
0.10
s 5 100,000
Hodges made $100,000 in sales.
I can verify my solution by substituting 100,000 in the equation.
20,000 1 0.10(100,000) 5 30,000
20,000 1 10,000 5 30,000
30,000 5 30,000
Chapter 7 Assignments • 129
© 2011 Carnegie Learning
130 • Chapter 7 Assignments
Lesson 7.4 Assignment
Name_________________________________________________________ Date__________________________
Solving in Big-Time Style
Using Two-Step Equations
1. Drake’s Drugstore is getting ready for the upcoming summer season. The manager of the store
wants to add lawn chairs to the stock. He asks the buyer to determine the two lowest priced
wholesalers of lawn chairs. The table shows the data that the buyer collects from two wholesalers.
Packs of
Chairs
Price from
Wholesaler A
(dollars)
Price from
Wholesaler B
(dollars)
1
$90.99
$98.99
2
$173.98
$179.98
3
$256.97
$260.97
4
$339.96
$341.96
Use the table to answer each question.
a. At Wholesaler A, what is the difference in price between two packs of chairs and one pack of
© 2011 Carnegie Learning
chairs? What is the difference in price between four packs of chairs and three packs of chairs?
173.98 2 90.99 5 82.99
339.96 2 256.97 5 82.99
The difference in price between the packs of chairs is $82.99.
b. How does the total cost of buying chairs from Wholesaler A change when the number of packs
of chairs increases by one pack (except the first pack)?
The total cost to buy the chairs increases by $82.99 for each addition pack of chairs except
the first pack.
Chapter 7 Assignments • 131
Lesson 7.4 Assignment
page 2
c. Let p represent the total number of packs of chairs bought from Wholesaler A. Write an
expression to calculate any number of packs of chairs. Explain your reasoning.
90.99 1 82.99(p 2 1)
I start with the first pack of chairs which costs $90.99. Then I multiply 82.99 by the total
number of packs minus one because the first pack of chairs must be subtracted because it
costs $90.99 rather than $82.99
d. Simplify your expression.
90.99 1 82.99p 2 82.99
8 1 82.99p
e. Use your expression to determine what it would cost to buy eight packs of chairs from
Wholesaler A? Explain your reasoning.
8 1 82.99p
8 1 82.99(8) 5 t
8 1 663.92 5 t
671.92 5 t
It would cost $671.92 to buy eight packs of chairs from Wholesaler A.
Wholesaler A if the cost is $505.94.
8 1 82.99p 5 505.94
8 2 8 1 82.99p 5 505.94 2 8
82.99p 5 497.94
82.99p _______
5 ​ 497.94 ​ 
​ _______ ​ 
82.99
82.99
p 5 6
The drugstore bought 6 packs of chairs from Wholesaler A for a cost of $505.94.
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f. Use your expression to determine the number of packs of chairs the drugstore bought from
Lesson 7.4 Assignment
page 3
Name_________________________________________________________ Date__________________________
g. What is the cost to buy one pack of chairs from Wholesaler B?
The first pack of chairs costs $98.99.
h. At Wholesaler B, what is the difference in price between two packs of chairs and one pack of
chairs? What is the difference in price between four packs of chairs and three packs of chairs?
179.98 2 98.99 5 80.99
341.96 2 260.97 5 80.99
The difference in price between the packs of chairs is $80.99
i. Let p represent the total number of packs of chairs bought from Wholesaler B. Write an
expression to calculate any number of packs of chairs. Explain your reasoning. Remember to
simplify your expression.
98.99 2 80.99(p 2 1)
98.99 2 80.99p 2 80.99
18 1 80.99p
j. Use your expression to determine what it would cost to buy eight packs of chairs from
© 2011 Carnegie Learning
Wholesaler B? Explain your reasoning.
18 1 80.99p
18 1 80.99(8) 5 t
18 1 647.92 5 t
t 5 665.92
It would cost $665.92 to buy eight packs of chairs from Wholesaler B.
Chapter 7 Assignments • 133
Lesson 7.4 Assignment
page 4
k. At how many packs of chairs will the price to buy them from Wholesaler A by the same as the
price to buy them from Wholesaler B? Write an equation and explain your reasoning.
8 1 82.99p 5 18 1 80.99p
8 2 8 1 82.99p 5 18 1 80.99p 2 8
82.99p 5 10 1 80.99p
82.99p 2 80.99p 5 10 1 80.99p 2 80.99 p
2p 5 10
p 5 5
The price of the chairs would be the same for 5 packs of chairs.
l. The manager wants to buy at least seven packs of chairs. Which wholesaler should the
drugstore use this year? Explain your reasoning.
The drugstore should use Wholesaler B. Wholesaler A costs less than Wholesaler B only for
fewer than five packs of chairs, at which the cost is the same. For more than five packs of
© 2011 Carnegie Learning
chairs, Wholesaler B costs less.
134 • Chapter 7 Assignments
Lesson 7.4 Assignment
page 5
Name_________________________________________________________ Date__________________________
2. The manager of a home store is buying lawn chairs to sell at his store. Each pack of chairs
contains 10 chairs. The manager will sell each chair at a markup of 20% of the wholesale cost,
plus a $2.50 stocking fee.
a. Write an equation that represents the retail price of a chair, r, in terms of the wholesale price, w.
r 5 1.20w 1 2.50
b. Use your equation to calculate the retail price of the chair if the wholesale price is $8.40.
r 5 1.20(8.40) 1 2.50 5 12.58
The retail price of the chair will be $12.58.
c. Use your equation to calculate the retail price of the chair if the wholesale price is $8.55.
r 5 1.20(8.55) 1 2.50 5 12.76
The retail price of the chair will be $12.76.
© 2011 Carnegie Learning
d. Use your equation to calculate the wholesale price of the chair if the retail price is $12.66.
12.66 5 1.20w 1 2.50
12.66 2 2.50 5 1.20w 1 2.50 2 2.50
1.20w
10.16 ​ 5​
  _______
 
 
  
​
​ ______
1.20
1.20
8.47 5 w
The wholesale price of the chair is $8.47.
Chapter 7 Assignments • 135
Lesson 7.4 Assignment
page 6
e. Use your equation to calculate the wholesale price of the chair if the retail price is $13.30.
13.30 5 1.20w 1 2.50
13.30 2 2.50 5 1.20w 1 2.50 2 2.50
1.20w   
10.80 ​ 5 ​ 
  ______
 
​
​ ______
1.20
1.20
9.00 5 w
The wholesale price of the chair is $9.00.
© 2011 Carnegie Learning
136 • Chapter 7 Assignments
Lesson 7.5 Assignment
Name_________________________________________________________ Date__________________________
We’re Shipping Out!
Solving and Graphing Inequalities in One Variable
1. Taneisha has decided to go on a new cell phone plan. She makes $150 per month babysitting
so she has to be careful of how much she spends on the plan.
a. If the plan costs $55 per month plus $0.20 for each text, write and solve the inequality
to determine the maximum number of texts she can make and still afford to pay the bill.
55 1 0.20t # 150
55 2 55 1 0.20t # 150 2 55
0.20t # 95
0.20t ​ #
  _____
​  95  ​ 
​ _____
0.20
0.20
t # 475
Taneisha can make at most 475 texts and still afford to pay the bill.
© 2011 Carnegie Learning
b. What is the least amount of texts Taneisha can make?
Taneisha can make 0 texts in one month.
c. Graph the solution set for the number of texts Taneisha can make in one month.
0 < t < 475
0
50 100 150 200 250 300 350 400 450 500
Chapter 7 Assignments • 137
Lesson 7.5 Assignment
page 2
d. Choose a value from the solution set and verify that it is a solution.
I can choose 200 and substitute for t in the inequality.
55 1 0.20(200) # 150
55 1 40 # 150
95 # 150 is true.
The solution 200 makes the inequality true.
2. Taneisha has found a different cell phone plan that she thinks might be better for her. This plan
charges $90 plus $0.15 for every text over 100. Write an expression to represent the monthly cost
of this plan.
90 1 0.15(t 2 100)
a. Simplify the expression for the cost of this plan.
90 1 0.15(t 2 100) 5 90 1 0.15t 2 15 5 75 1 0.15t
b. Taneisha wants to determine the number of texts for which the cost of this plan is less than the
75 1 0.15t , 55 1 0.20t
75 2 75 1 0.15t , 55 1 0.20t 2 75
0.15t , 220 1 0.20t
0.15t 2 0.20t , 220 1 0.20t 2 0.20t
20.05t , 220
220
20.05t ​ .
  ​ ______ 
 ​ 
​ _______
20.05
20.05
t . 400
If Taneisha makes more than 400 texts, the new plan will be less expensive than the original plan.
138 • Chapter 7 Assignments
© 2011 Carnegie Learning
cost of the original plan. Write the inequality for this situation and solve.