SOLUTION: Truck A is priced at $450 and gets 25 miles per gallon. Truck B is priced at $650 and gets 35 miles per gallon. If gasoline cost $4 per gallon how many miles would I have to drive

Algebra ->  Equations -> SOLUTION: Truck A is priced at $450 and gets 25 miles per gallon. Truck B is priced at $650 and gets 35 miles per gallon. If gasoline cost $4 per gallon how many miles would I have to drive       Log On


   

Question 1139195: Truck A is priced at $450 and gets 25 miles per gallon. Truck B is priced at $650 and gets 35 miles per gallon. If gasoline cost $4 per gallon how many miles would I have to drive to make truck B the better buy
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Truck A cost function:   A(x) = 450 + 4*(x/25)


Truck B cost function:   B(x) = 650 + 4*(x/35)


Truck B is better to buy if


    B(x) < A(x),        which means


    650+%2B+4%2A%28x%2F35%29 <  450+%2B+4%2A%28x%2F25%29


Simplify step by step and solve for x:


    650 - 450 < 4%2Ax%2F25%29 - 4%2A%28x%2F35%29

    200       <  4%2Ax%2F25%29 - 4%2A%28x%2F35%29


Divide by 4 both sides


    50 < x%2F25 - x%2F35 = %287x%29%2F175 - %285x%29%2F175 = 2x%2F175


So, you have


    %282x%29%2F175 > 50.


Multiply both sides by  175%2F2. You will get


    x > %2850%2A175%29%2F2 = 4375.


It is your  ANSWER :  If x > 4375 miles, then truck B is better to buy than truck A.


Solved, explained and completed.