After how many miles with the cost of the two rental car companies be the same?

Question

Rental car A charges $125 per week with a $0.04 charge per mile and rental car company B charges $59 per week with a $0.10 charge per mile. After how many miles with the cost of the two rental car companies be the same?

Answer 1

The cost of each car is the 'sunk' weekly cost plus the cost per mile.  That equations look like this

 

 

125 + (0.04 x M)   <-- where M is the number of miles 

 

59 + (0.10 x M)

 

 

You want to to set these equations equal to each other and solve for M and this will give you the breakpoint Mile where each company is charging you the same amount for the rental.  Try doing it yourself before you scroll down to see me working out this problem.

 

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ok here goes

 

125 + 0.04M = 59 + 0.10M

125-59         = 0.10M - 0.04M

66                = 0.06M

66/0.06        = 0.06M/0.06

1100            = M

 

If you drive exactly 1100 miles then both car rental companies will charge you the same.  Put that mileage back into the original 2 equations to check your work.

 

All the best

 

Lori