Question

Mr. Engen rented a car for 35.00 a day and 0.45 a mile . He had the car for 2 days and paid 166.75 . How many miles did he drove ?

Answer 1

d = days rented for

m = miles driven for

so the cost of the car is 35 bucks a day and 45 cents or $0.45 per mile driven, let's check it out for say a few days

1st day, 3 miles......................35(1) + 0.45(3)

2nd day, 2 miles..................35(2) + 0.45(2)

3rd day, say 5 miles............35(3) + 0.45(5)

dth day, and m miles..........35d + 0.45m

so the cost function could be written as C = 35d+0.45m.

now, we know for 2 days, d = 2, it cost 166.75 bucks, so

$\bf C=35d+0.45m\implies \stackrel{C}{166.75}=35(\stackrel{d}{2})+0.45m\\\\\\166.75=70+0.45m\implies 96.75=0.45m\\\\\\\cfrac{96.75}{0.45}=m\implies 215=m$