Bill wants to rent a car. rental company a charges $35 per day plus $0.10 per mile driven. rental company b charges $25 per day plus $0.15 per mile driven. after how many miles driven will the price charged by each company be the same?

You gotta pick number (Miles) that give you higher figure for 0.15 and lower figure 0.10 so that the actual answer comes same after adding them with per day charges.

Let's pick 100 miles for A and B,

A, 0.10x 100 = $10
= ($35 + $10)
=$45

B, 0.15 x 100 = $15
= ($25 + $15)
=$40
Well, it ain't giving us same charge, so we should go higher miles

Let's take 200 miles this time.

A, 0.10x 200 = $20
= ($35 + $20)
=$55

B, 0.15 x 200 = $30
= ($25 + $30)
=$55

after 200 miles.