SOLUTION: Phuong Dan's car averages 8 more miles per gallon on the highway than it does in city driving. Last week he drove 160 highway miles and 180 city miles and used 12.5 gallons of gas.

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Question 165669: Phuong Dan's car averages 8 more miles per gallon on the highway than it does in city driving. Last week he drove 160 highway miles and 180 city miles and used 12.5 gallons of gas. How many miles per gallon does the car get in city driving?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call x the miles per gallon in city driving and x=8 the miles per gallon highway driving...
so know that the miles driven divided by the number miles per gallon will give us the # of gallons used.
therefore we have 160%2F%28x%2B8%29%2B180%2Fx=12.5 finding a common denominator of x(x+8) on the left side of the equation we get
%28160x%2B180x%2B1440%29%2Fx%28x%2B8%29=12.5 cross multiplying and adding like terms we get 340x%2B1440=12.5%28x%5E2%2B8x%29 distributing the right side and putting everything = to 0 we get 12.5x%5E2-240x-1280 when you plug this into the quadratic formula you arrive at x=24 and x=-4.8 so we throw out the negative answer and we are left with x=24
so since x is the miles per gallon in city driving the we get 24 miles to the gallon in city driving as the answer. which would make highway mpg at 32