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?

At 200 miles, both companies will have charged the same price.  This is because if you set up an equation where 35 plus 0.1(m) is equal to 25 plus 0.15(m), you subtract 25 from each side and are left with 10 plus 0.1(m) being equal to 0.15(m).  You then subtract the 0.1 from each side and are left with 10 being equal to 0.05(m), where m must then equal 200.