Q: A movie theater sold 785 tickets for a total of $$3280. Adult tickets cost 5 $$each and child tickets cost $$2 each. Which system of equations represents this scenario if x$ is the number of adult tickets and y$ is the number of child tickets?

$$\begin{cases} x + y = 785 \\ 5x + 2y = 3280 \end{cases}$$

Q: Rob has 40 coins, all dimes and quarters, worth $$7.60. Let x$ be the number of dimes and y$ the number of quarters. Which system of equations models this situation?

$$\begin{cases} x + y = 40 \\ 0.10x + 0.25y = 7.60 \end{cases}$$

Question 1

A gym charges a $$25 sign-up fee and 15 $$per month. Which equation in slope-intercept form models the total cost $$y$$ after $$x$$ months?

Accepted Answer

$$y = 15x + 25$$

Question 2

A movie theater sold 785 tickets for a total of $$3280. Adult tickets cost 5 $$each and child tickets cost $$2 each. Which system of equations represents this scenario if x$ is the number of adult tickets and y$ is the number of child tickets?

Accepted Answer

$$\begin{cases} x + y = 785 \ 5x + 2y = 3280 \end{cases}$$

Question 3

Rob has 40 coins, all dimes and quarters, worth $$7.60. Let x$ be the number of dimes and y$ the number of quarters. Which system of equations models this situation?

Accepted Answer

$$\begin{cases} x + y = 40 \ 0.10x + 0.25y = 7.60 \end{cases}$$

Question 4

The sum of Claudia’s age and Pedro’s age is 14 years. Claudia is 6 years older than Pedro. What are their ages?

Accepted Answer

Claudia is 10 years old, Pedro is 4 years old.

Question 5

A rectangle has a perimeter of 80 cm. Its length is 4 cm longer than its width. What are the dimensions of the rectangle?

Accepted Answer

Length = 22 cm, Width = 18 cm

Question 6

Sally starts with $$150 and saves 5 $$per week. Lucie starts with $$200 and saves 3 $$per week. After how many weeks will they have the same amount saved?

Accepted Answer

25 weeks

Question 7

The sum of the squares of two numbers is 130, and the difference of their squares is 32. What are the two numbers?

Accepted Answer

9 and 7

Question 8

A rectangular holding pen for cattle has a perimeter of 92 feet and an area of 525 square feet. What are the dimensions of the pen?

Accepted Answer

Length = 31 ft, Width = 15 ft

Question 9

A collection of nickels and quarters is worth $2.85. There are 3 more nickels than quarters. How many nickels are there?

Accepted Answer

15 nickels

Question 10

The range of a radio tower is bounded by $$x^2$$ + $$y^2 = 1620$. A highway is modeled by y$$ = -\frac{1}{3}x + 30$$. For what values of x$ does the highway pass through the broadcast range?

Accepted Answer

$$-36 \leq x \leq 27$$

Question 11

Serena bought 10 picture frames, some small ($$3 each) $$and some large ($$5 each$$), spending $36 in total. How many large frames did she buy?

Accepted Answer

3 large frames

Question 12

The cost of 5 squash and 2 zucchini is $$1.32. Three squash and 1 zucchini cost 0.75. $$What is the cost of one squash?

Accepted Answer

$$0.21$$

Question 13

The equation $$y = 4x - 9 is in $$which form?

Accepted Answer

Slope-intercept form

Question 14

A rectangle has a length that is 1 inch more than twice its width. If the area is 36 square inches, what is the length?

Accepted Answer

9 inches

Question 15

Judy worked 8 hours and Ben worked 10 hours for a total of $$80. When Judy worked 9 hours and Ben 5 hours, their combined pay was 65. $$What is Ben’s hourly rate?

Accepted Answer

$$5$$

Question 16

The sum of the squares of two numbers is 20, and their product is 8. What are the two numbers?

Accepted Answer

2 and 4

Question 17

The perimeter of a rectangle is 48 inches. The length is 3 times the width. What is the area of the rectangle?

Accepted Answer

144 square inches

Question 18

The supply and demand for a CD at Jim’s Music Store are given by $$d = 24t + 180$$ and $$s = 800 - 100t$$, where $$t is $$weeks. After how many weeks will supply equal demand?

Accepted Answer

5 weeks

Question 19

A rectangular room has an area of 135 square feet. The width is 6 feet less than the length. What is the length?

Accepted Answer

15 feet

Question 20

The talent show committee sold 530 tickets in advance. Student tickets cost $$3 each and adult tickets 4 $$each. If the total receipts were $1740, how many adult tickets were sold?

Accepted Answer

380 adult tickets

Systems of Equations and Applications – Step-by-Step Study Guidance

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