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twice last month, judy carter rented a car in Fresno, California and traveled around the southwest on business. the car rentel agency rents its cars for a daily fee, plus an additional charge per mile driven. judy recalls that her first trip lasted 4 days she drove 370 miles and the rental cost her $244.50. on her 2nd business trip she drove 190 miles in 3 days and paid $161.50 for the rental. find the daily fee and the millage charge.

Respuesta :

Create a system of 2 equations

Let x be daily fee and y the mileage charge, then

4x + 370y = 244.50...........(1)

3x + 190y = 161.50..............(2)

If we multiply (1) by 3 and (2) by -4 and add the 2 equations we eliminate x:-

12x + 1110y = 733.50

-12x - 760y = -646 Adding :-

350y = 87.5 so y = 0.25

Plugging y = 0.25 into eqation (1) we get 4x = 244.50 - 0.25 * 370

giving x = 38

Answer is daily fee = $38 and mileage charge = $0.25 per mile.

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Let daily rate be x and mileage be y.

4x + 450y = 240.50

3x + 200y = 146.00

Multiply 1st equation by 3 and second equation by 4

12x + 1350y = 721.50-----(1)

12x + 800y = 584.00 ------(2)

Subtracting you get:

550 y = 137.50 or y = 0.25

Substituting value for y in equation (2) you get

x = 32.00

Daily rate = $ 32.00 and mileage = $ 0.25