EOI Systems of equations/inequalities Name _______________________ hour ______

1. Profits are equal to sales, S, minus expenses, E. If expenses are equal to travel, T, plus materials, M, which system of equations models this situation?

a) P = S - E b) P = S - E c) P = S + E d) P = S + E

E = T + M E = T + M E = T - M E = T – M

2. Tyrone spent no more than $1,500 to buy a television and a DVD player. The television and the DVD player each cost at least $100. Which system of inequalities models the amount of money Tyrone spent to buy the television, T, and the DVD player, D?

a) T+D1500 b) 0T+D1500 c) 0T+D1500 d) T+D>1500

T4D D4T T4D D4T

T100 T100 T100 T100

D100 D100 D100 D100

3. Meredith invests $50,000 in her new business. It costs the company $10 to produce each unit, which is sold for $15. Let C represent the cost and R represent the revenue for x units. Which statement is true about the graphs of the equations C=50,000+10x and R=15x?

a) Both slopes are positive. b) Both slopes are negative.

c) One slope is positive, and the other is zero. d) One slope is negative, and the other is positive.

4. The vertices of a triangle are (2,1), (4,4), and (6,2). Which system of inequalities describes the interior of the triangle?

a) 4y > x + 2 b) 4y > 2x - 1 c) 2y > x d) 2y > x

3y < 2x - 1 2y < 3x - 4 2y < 3x - 4 3y < 2x - 1

y < 8 - x y < 8 - x y < 8 - x y < 8 – x

5. Amy ordered k ketchup packets, m mustard packets, and r relish packets for the concession stand at school. She ordered twice as many mustard packets as relish packets and 100 more ketchup packets than mustard packets. She ordered a total of 1,000 packets. The situation can be modeled by this system of equations shown below. How many relish packets did Amy order?

m = 2r

k = 100 + m

k + m + r = 1,000

a) 180 b) 300 c) 360 d) 460

6. Sam and Dan work for Mountain Brook bottled water distributors. Sam just started and makes $300 per week plus $45 for each new customer who signs a contract. Dan has been working for 9 months and now makes $325 per week plus $60 for each new customer. Which system of equations best models this situation if SS represents Sam’s salary, SD represents Dan’s salary n is the number of new customers?

a) SS = 325 + 60n b) SS = 300 + 45n c) SS = 345 + n d) SS = 300 + 45n

SD = 300 + 45n SD = 325 + 9n SD = 385 + n SD = 325 + 60n

7. Karen traveled almost 350 miles in under 7 hours of highway driving. She stopped for a brief rest that was not included in her driving time. She averaged 60 mph for the first part of her trip and 50 mph for the second part of the trip. Which system of inequalities can be used to determine how many hours Karen spent driving in each part of her trip if A is the time she spent on the first leg and B is the time on the second leg?

a) A + B = 7 b) A - B = 7 c) A + B = 7 d) A + B = 350

A + B = 350 60A + 50B = 7*350 60A + 50B = 350 60A – 50B = 7

8. A company produces cell phones. It costs at least $35 plus $14.50 per cell phone to produce the items. The maximum retail price per cell phone is $125. Which of the systems, where c is the cost and n is the number of cell phones produced or sold, represents the situation?

a) c ≥ $35 + $14.50n b) c ≤ $35 + $14.50n c) c ≥ $14.50n d) c ≥ $35n + $14.50

c ≤ $125 c ≥ $125 c ≤ $125 + $35 c ≤ $125

9. The prom committee is selling tickets for $35 if bought ahead of time or $45 at the door. They hope to sell at least 550 tickets in all and hope to make at least $2000. Which system of inequalities represents this situation if A is the number of presale tickets sold and B is the number sold at the door?

a) A + B ≤ 550 b) A + B ≥ 550 c) A + B = 550 d) A + B ≥ 2000

35A + 45B ≤ 2000 35A + 45B ≥ 2000 35A + 45B = 2000 35A + 45B ≤ 2000

10. A circuit has a current of (8+7i) amps, and another circuit has a current of (5-3i) amps. What is the difference between the currents of the two circuits? a) (3-4i) amps b) (3+4i) amps c) (3-10i) amps d) (3+10i) amps