COORDINATE ALGEBRA: UNIT 2 EOC REVIEW

1. Reasoning With Equations and Inequalities
A manager is comparing the cost of buying ball caps with the company emblem from two different companies.
·  Company X charges a $50 fee plus $7 per cap.
·  Company Y charges a $30 fee plus $9 per cap.
For what number of ball caps will the manager’s cost be the same for both companies?
A. 10 caps C. 40 caps
B. 20 caps D. 100 caps / 2. Reasoning With Equations and Inequalities
A shop sells one-pound bags of peanuts for $2 and 3-pound bags of peanuts for $5. If 9 bags are purchased for a total cost of $36, how many tree-pound bags were purchased?
A. 3
B. 6
C. 9
D. 18
3. Which graph would represent a system of linear equations that has multiple common coordinate pairs?

4. Which graph represents the solutions to x > 3?
5. Which pair of inequalities is shown in the graph?

A,
B.
C.
D.
6, What is the x-value of the solution to this system of equations?
3x + 2y = 6
2x + y = 2
A. x = −2 B. x = 10/7
C. x = 2 D. x = 4
7. This coordinate plane shows the graph of an equation:
Which statement about the solutions of the equation MUST be true?
A If the x-value of a solution is positive, then the corresponding y-value is negative.
B If the x-value of a solution is negative, then the corresponding y-value is positive.
C There is no solution for which both the x-value and the y-value are integers.
D There is only one solution for which both the x-value and the y-value are integers.

Free Response

8. You want to rent a truck for a home improvement project. You think you will only need the truck for 3 hours. You checked the prices of truck rentals from Home Depot and Lowe’s and are trying to decide which one you should pick. Home Depot rents their trucks for a fee of $15 and $16 per hour. Lowe’s rents their trucks for $7 fee and charges $5 for every 15 minutes. Which truck rental should you choose and why?

9. The drama club is having a car wash as a fundraiser. They wash x cars at $5 each and y trucks at $8 each. They will wash no more than 30 cars and 40 trucks. They need to make at least $250.

(a)  Write a system of inequalities for this scenario.

(b)  Which graph shows the correct graph of the scenario?

A B

C D

ANSWER KEY:

1) A

2) B

3) B

4) C

5) A

6) A

7) B

8. You want to rent a truck for a home improvement project. You think you will only need the truck for 3 hours. You checked the prices of truck rentals from Home Depot and Lowe’s and are trying to decide which one you should pick. Home Depot rents their trucks for a fee of $15 and $16 per hour. Lowe’s rents their trucks for $7 fee and charges $5 for every 15 minutes. Which truck rental should you choose and why?

For three hours, Home Depot will be the better choice at a total cost of $63, compared to Lowe’s total cost of $67.

Will the same company always be the better choice?

Unless you are renting a truck for only one hour, Home Depot is the cheaper choice. Lowe’s rental for one hour has a total of $27. Home Depot costs $31 for one hour. The two companies cost the same ($47) when renting for two hours. After two hours, Home Depot will have a cheaper overall cost when comparing to Lowe’s.

9. The drama club is having a car wash as a fundraiser. They wash x cars at $5 each and y trucks at $8 each. They will wash no more than 30 cars and 40 trucks. They need to make at least $250.

(a) Write a system of inequalities for this scenario.

(c)  Which graph shows the correct graph of the scenario? B

A B

C D