AnswersSSCR 26 Math Essentials ASolving Real-World Multistep Equations

Solving Real-World Multistep Equations Answers

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1
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Tamara bought yarn for $39 and 2 pairs of knitting needles. Her total cost for the yarn and knitting needles was $69. Tamara writes an equation that represents the cost of each pair of knitting needles. If k represents the cost of each pair of knitting needles, which statements about verifying the value of k are true? Check all that apply.

A
Tamara should substitute into the equation .
Option A
B
After she substitutes the correct value for k into the equation, Tamara should find that the left side of the equation is equal to the right side.
C
Tamara should substitute into the equation .
Option C
D
After she substitutes the correct value for k into the equation, Tamara should find that the left side of the equation is not equal to the right side.
E
To verify the solution to the equation, Tamara multiplies the solution by 2 and then adds it to 39. Then, she checks that it is equal to 69.
F
To verify the solution to the equation, Tamara adds the solution to 2 and then adds it to 69. Then, she checks that it is equal to 39.
2
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Amie works 6 hours each Saturday and 4 hours each Monday. She also makes $20 a week as a dog walker. She makes a total of $130 each week. If h represents Amie’s hourly rate, which equation can be used to find Amie’s hourly rate?

A
6 h + 20 = 130
Option A
B
(6 + 4) h = 130
Option B
C
(6 + 4) h + 20 = 130
Option C
D
4 h + 20 = 130
Option D
3

The cost to rent a rug-cleaning machine from the supermarket is $23 per day. The supermarket charges a check-out fee of $45 for the rental. Tristanne spent $137 to rent the rug-cleaning machine. If d represents the number of days Tristanne rents the machine, which equation can be used to find the value of d?

A
23 d = 137
Option A
B
23 d + 45 = 137
Option B
C
45 d = 137
Option C
D
45 d + 23 = 137
Option D
4

The Star television costs $750 more than the Jupiter television. The two models cost $2,600 all together. Sandra writes an equation to find the cost of the two models. If c represents the cost of the Jupiter television, which of the following would be true when verifying the solution of the equation? Check all that apply.

A
Sandra substitutes into the equation .
Option A
B
Sandra substitutes into the equation .
Option B
C
Sandra finds a true statement after substituting 925 into the equation.
D
Sandra finds a false statement after substituting 925 into the equation.
E
When Sandra evaluates the equation with c = 925, she subtracts 750 from 925. Then, she adds that sum to 925. She finds that the value is not equal to 2,600.
F
When Sandra evaluates the equation with c = 925, she adds 925 to 750. Then, she adds that sum to 925. She finds that the value is 2,600.
5

In a basketball tournament, team A scored 6 more points than 3 times as many points as team B scored. Team C scored 45 more points than team B scored. The combined scores for all three teams was 476 points. Which statement about the number of points is true?

A
Team A scored 85 points.
B
Team A scored 255 points.
C
Team C scored 261 points.
D
Team C scored 130 points.
6

A two-day moving truck rental from Best Rentals costs $60 and $0.35 per mile driven. A two-day moving truck rental from Easy Movers costs $80 and $0.25 per mile driven. Let m represent the number of miles driven. Which equation can be used to find the number of miles for which the rentals would cost the same amount?

A
60 + 0.35 m = 80 + 0.25 m
Option A
B
60 m + 0.35 = 80 + 0.25 m
Option B
C
60 + 0.35 m = 80 m + 0.25 m
Option C
D
60 m + 0.35 = 80 m + 0.25
Option D
7

A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?

A
7 x + 200 = 17,700
Option A
B
6 x + 200 = 17,700
Option B
C
7 x minus 200 = 17,700
Option C
D
6 x minus 200 = 17,700
Option D
8

The perimeters of the square and the regular pentagon are equal.What is the perimeter of each polygon?

Question illustration
A
12
B
15
C
42
D
60
9

The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by . Which equation can be used to find the value of x?

Question illustration
A
x = 3 (x + 1)
Option A
B
3 x = 4 (x + 1)
Option B
C
4 x = 3 (x + 1)
Option C
D
x = x + 1
Option D
10

The perimeter of a rectangle is 64 feet. The length of the rectangle is 3 times the width of the rectangle. If w represents the width of the rectangle, the equation that represents the perimeter is . Which shows the first step that should be taken to verify that the width of the rectangle is 8?

Question illustration
A
2 (8) + 2 (8) = 64
Option A
B
2 (3 + 8) + (2 + 8) = 64
Option B
C
2 (3 (8)) + 2 (8) = 64
Option C
D
2 (3 + 8) + 2 (8) = 64
Option D
11

Joan is buying airline tickets for her family. Each airline ticket costs $232 with a baggage fee of $13. The airline charges a booking fee of $45 for the entire set of tickets. Joan spent a total of $1,515. If x represents the number of tickets, which equation can be used to find the value of x?

A
245 + 45 x = 1,515
Option A
B
232 x + 45 x = 1,515
Option B
C
232 x + 45 = 1,515
Option C
D
245 x + 45 = 1,515
Option D
12

Caitlyn spends $17 at the store. She buys a mop for $5 and 3 bottles of floor cleaner. If x represents the cost of each bottle of cleaner, the equation that can be used to find the value of x is . Which shows the first step that should be taken to verify that $4 is the solution to the equation?

Question illustration
A
3 (4) minus 5 = 17
Option A
B
3 (4) = 17 + 4
Option B
C
3 (4) + 5 = 17 + 5
Option C
D
3 (4) + 5 = 17
Option D
13

Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an initial fee of $10.00 and an hour rate of $10.50. At how many hours of instruction will the price for each instructor be the same?

A
2 hours
B
3 hours
C
20 hours
D
30 hours
14

Kendall scored 3 times as many points as Abdul scored in a basketball game. Otis scored 5 more points than Abdul scored. The three players scored 45 points all together. How many points did each player score?

A
Kendall: 24 points; Abdul: 13 points; Otis: 8 points
B
Kendall: 8 points; Abdul: 8 points; Otis: 8 points
C
Kendall: 24 points; Abdul: 8 points; Otis: 13 points
D
Kendall: 8 points; Abdul: 13 points; Otis: 24 points

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