Eighth Grade math

Question

Your family is renting a car for the weekend.

● Zoom Rentals ​charge an initial fee of $125 then $0.04 per mile.

● Super Wheels ​charge an initial fee of $59 then $0.10 per mile.

How many miles would Your family have to drive for the cost to be the same?

Answer 1

Hi Marionnice,

We want to see where these two equations equal each other, but initially let's find the equations of each line.

1) y1 = 0.04 (x) + 125

2) y2 = 0.10 (x) + 59 (I used y2 to just say that we were working with a second equation)

But we want to solve for when y1=y2.

So we have:

0.04 (x) + 125 = 0.10 (x) + 59 (subtract 59 from each side)

0.04 (x) +125 - 59 = 0.10 (x)

0.04 (x) + 66 = 0.10 (x) (Now, subtract factors of x)

66 = 0.10(x) - 0.04(x)

66 = 0.06 (x) (divide both sides by 0.06 to solve for x)

(66/0.06) = (0.06x / 0.06) = x

So x = 1,100

So at 1,100 miles, the family would have spent the same amount of money on rental cars.

As a side note: If the family drives fewer miles, the $59 initial rate rental (Zoom) would be a better deal. If the family drove more than $1,100, they would be better off with the $125 initial rate rental (Super Wheels).