Question

A. Sam needs to rent a car for a one-week trip in Oregon. He is considering two companies. A+ Auto Rental charges $175 plus $0.10 per mile. Zippy Auto Rental charges $220 plus $0.05 per mile. Write an equation relating the rental cost for each company to the miles driven.

b. Graph the equation. (You don't need to do this)
c. Under what circumstances is the rental cost the same for both companies? What is that cost?
d. Under what circumstances is renting from Zippy cheaper than renting from A+?
e. Suppose Sam rents a car from A+ and drives it 225 miles. What is his rental cost?

2. Maggie lives 1,250 meters from school. Ming live 800 meters from school. Both girls leave for school at the same time. Maggie walks an average speed of 70 meters per minute, while Ming walks at an average speed of 40 meters per minute. Maggie's route takes her past Ming's house.
a. Write equations the show Maggie and Ming's distances from school 't' minutes after they leave their homes.
Answer parts (b)-(d) by writing and solving equations or inequalities.
b. When, if ever, will Maggie catch up with Ming?
c. How long will maggie remain behind Ming?
d. At what times is the distance between the two girls less than 20 meters?

Answer 1

1)
a. A+ Auto Rental equation --> y = 175 + .1x -- x equals miles
Zippy Auto Rental --> y = 220 + .05x

c. Set both equations equal to each other --> 175 + .1x = 220 + .05x
.05x = 45
x = 900 (miles)

d. Renting from Zippy is cheaper if Sam will drive more than 900 miles.

e. His rental cost will be y(225) = 175 + .1(225) = $197.5

2)
a. Maggie's equation --> y = 1250 - 70t
Ming's equation --> y = 800 - 40t

b and c (same answer). Set both equations equal to each other --> 1250 - 70t = 800 - 40t --> 450 = 30t --> t = 15 minutes

d. Maggie --> 20 > 1250 - 70t --> 70t > 1230 --> t > 17.6(rounded) minutes
Ming --> 20 > 800 - 40t --> 40t > 780 --> t > 19.5 minutes

13. y = -4
14. y = -23
15. if y = (1/2)x - 4, y = 8
16. y = -8
17. if y = (2/3)x - 12; y = -24
18. y = 3/4

23. m = 7, x-int = -3 (set x = 0), y-int = 3/7 (set y = 0) --> "m" = slope, because the equation is y = mx + b
24. m = -3, x-int = 4, y-int = 4/3
25. m = 2/3, x-int 12, y-int = -18
26. m = -1/4, x-int = -5, y-int = -20
27. m = -17, x-int = 3/4, y-int = 3/68
28. m = -3/5, x-int = -6, y-int = -10