Having problem setting this up and solving

Question

Your new hybrid car gets 40 mpg in the city and 32 mpg on the highway. The amount of gas you use, G(in gal), is given by G=1/40c + 1/32h where c is the number of city miles driven and h is the number of highway miles driven. If you drove 150 miles in the city and used 8.5 gallons of gas, how many highway miles did you drive?

Answer 1

p.s., slight correction to Mark M.'s post:

 

G = 1/40(c) + 1/32(h)             substitute values
8.5 = 1/40(150) + 1/32(h)       simplify
8.5 = 3.75 + h/32                   subtract 3.75 from both sides
4.75 = h/32                            multiply both sides by 32
152 = h

 

You drove for one hundred fifty two miles on the highway.

 

Checking (very important):

  Is  (1/40)(150) + (1/32)(152) = 8.5   ?

          3.75         +    4.75       = 8.5   ?

                     8.5                 =   8.5   ? yes

Answer 2

G = 1/40(c) + 1/32(h)             substitute values

8.5 = 1/40(150) + 1/32(h)       simplify

8.5 = 3.75 + h/32                   subtract 3.75 from both sides

4.75 = h/32                            multiply both sides by 32

15.2 = h

 

You drove for fifteen and two tenths miles.