SOLUTION: A car rental agency charges a daily fee plus a mileage fee. Mr. Jones was charged $375 for 3 days and 500 miles. Mr. Smith was charged $470 for 4 days and 600 miles. What is the ag

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Question 249547: A car rental agency charges a daily fee plus a mileage fee. Mr. Jones was charged $375 for 3 days and 500 miles. Mr. Smith was charged $470 for 4 days and 600 miles. What is the agency's daily fee and what is their mileage fee?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
c = d+m

c = cost
d = daily charge
m = per mile charge

3d + 500m = 375
4d + 600m = 470

you need to solve these two equations simultaneously.

multiply first equation by 4 and multiply second equation by 3 to get:

12d + 2000m = 1500
12d + 1800m = 1410

subtract second equation from first equation to get:

200m = 90

divide both sides of this equation by 200 to get:

m = .45

substitute for m in first equation to get:

3d + 500m = 375 becomes:

3d + 500*.45 = 375

this becomes:

3d + 225 = 375

subtract 225 from both sides of the equation to get:

3d = 375 - 225 = 150

divide both sides of this equation by 3 to get:

d = 50

substitute for d and m in the second equation to get:

4d + 600m = 470 becomes;

4*50 + 600 * .45 = 470

simplify by performing indicated operations to get:

200 + 270 = 470

since this equation is true, the values for d and m are good.

your answer is:

the car rental agency charges 50 dollars a day and 45 cents per mile.