Question

A truck can be rented from Company A for $60 a day plus $0.60 per mile . Company B charges $30 a day plus $0.90 per mile to rent the same truck . Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answer 1

x = the number of miles

y = the total cost

Company A:

0.60x + 60 = y     [Company A charges $60 plus $0.60 per mile(x)]

Company B:

0.90x + 30 = y      [Company B charges $30 plus $0.90 per mile(x)]

To find the number of miles where the costs for both companies are the same, you can set the equations equal to each other as the costs(y) are the same:

y = y      Substitute the equations into "y" (substitute (0.60x + 60) and (0.90x + 30) into "y" since y = 0.60x + 60 and y = 0.90x + 30)

0.60x + 60 = 0.90x + 30   To find x, isolate/get the variable "x" by itself. Subtract 30 on both sides

0.60x + 60 - 30 = 0.90x + 30 - 30

0.60x + 30 = 0.90x      Subtract 0.60x on both sides to get "x" on one side of the equation

0.60x - 0.60x + 30 = 0.90x - 0.60x

30 = 0.30x      Divide 0.30 on both sides to get "x" by itself

100 = x     100 miles

(if you need to find out the cost where both companies cost the same, you can substitute/plug in the value of x into one of the equations.)

0.60x + 60 = y     Plug in 100 into "x" since x = 100

0.60(100) + 60 = y

120 = y        At 100 miles, both companies cost $120