Rate problem

Question

Barney was charged $111 for 3 days and 300 miles, while Mary was charged $197 for 5 days and 600 miles. What does the rental company charge per day and per mile if they charge a daily fee plus a mileage fee for renting their car?

Answer 1

Hello Ekaterina,

 

Let's let

d = $ rate per day

m = $ rate per mile

 

Based on Barney's charge

3d + 300m = 111

 

Based on Mary's charge

5d + 600m = 197

 

So our system of linear equations is

3d + 300m = 111

5d + 600m = 197

 

Multiply the 1st equation by -2

-6d - 600m = -222

5d + 600m = 197

 

Add the two equations together, eliminating the m variable

-d = -25

d = 25

 

Evaluate either original equation for d=25 and solve for m

3d+300m=111

3(25)=300m=111

75+300m=111

300m = 36

m = 0.12

 

The charge per day is $25.  The charge per mile is $0.12.