Question 165669
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/(x+8)+180/x=12.5}}} finding a common denominator of x(x+8) on the left side of the equation we get

{{{(160x+180x+1440)/x(x+8)=12.5}}} cross multiplying and adding like terms we get {{{340x+1440=12.5(x^2+8x)}}} distributing the right side and putting everything = to 0 we get {{{12.5x^2-240x-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