a word problem: A rental car costs a minimun charge plus a fixed charge permile

Question

   a word problem: A rental car costs a minimun charge plus a fixed charge permile driven. One customer was charged $60 for 160 miles ofuse. Another customer drove 280 miles and paid $90. Write anequation relating the total cost, C (in dollars), to the miledriven, x.    a word problem: A rental car costs a minimun charge plus a fixed charge permile driven. One customer was charged $60 for 160 miles ofuse. Another customer drove 280 miles and paid $90. Write anequation relating the total cost, C (in dollars), to the miledriven, x.

Explanation / Answer

To solve this you need to set up a system of equations. Let a be the fixed charge per x mile driven, and let b be theminimum charge. The first customer was charged $60 for 160miles use, so 60 = 160a + b is the equation for the firstcustomer. Likewise, the second customer drove 280 miles andpaid $90, so 90 = 280a + b. These two equations, (1)   60 = 160a + b and (2)   90 = 280a + b is the system of equations. Now all that's left isto solve for a and b to get the total cost C per x miledriven. It's easiest to solve this system by linear combination. Multiplying equation (1) by -1 gives (*) -60 = -160a - b. Nowadding equation (*) and (2) gives 30 = 120a. Thus a = 1/4 =0.25. Plugging a = 0.25 into either equation (1) or(2) and solving for b gives b = 20. Thus the total cost C in dollars for x mile driven is C =0.25x + 20.

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