math help equations

Question

Rapid Rental Car charges a $30 rental fee, $15 for gas, and $0.45 per mile driven. For the same car, Capital Cars charges $35 for rental and gas and $0.55 per mile.

 

Part 1 out of 2

For how many miles is the rental cost at both companies the same?

Answer 1

x=miles driven. First write the two companies’ equations and set them equal to each other. Cost rapid rental=30+15+0.45x. Cost Capital cars=35+0.55x

30+15+0.45x=35+0.55x Next combine like terms

45+0.45x=35+0.55x Subtract 35 from both sides

45-35+0.45x=35-35+0.55x

10+0.45x=0.55x Then subtract 0.45x from both sides

10+0.45x-0.45x=0.55x-0.45x

10=0.10x Divide both sides by 0.10

10/0.10= 0.1x/0.1

100=x

At 100 miles the rental costs for both companies are the same.