Question

Sam needs to rent a car for a one-week trip to oregon. he is considering two companies: a+ auto rental: $175 plus $0.10 per mile zippy auto rental: $220 plus $0.05 per mile. write and solve a system of equations to determine when the rental costs are the same for both companies.

Answer 1

Answer is at 900 miles the costs will be equal for both rental companies.

Step by step
Using slope intercept formula
y = mx + b

m = rate or slope, here it is the price per mile
x = the variable, the unknown miles
b = the flat rate or starting set cost


a+ rental
y = .10x + 175

zippy rental
y = .05 + 220

Make the two equations equal each other to solve

.10x + 175 = .05x + 220

Subtract .05x from each side to isolate variable

.10x - .05x + 175 = .05x - .05x + 220
Simplify

.05x + 175 = 220

Now subtract 175 from both sides to isolate constants

.05x + 175 - 175 = 220 - 175
Simplify

.05x = 45
Divide both sides by .05 to solve for x

.05/.05x = 45/.05

x = 900

So at 900 miles driven the costs will be the same.