Word question see below

Question

A car travel 213 miles on a trip. During 38 miles of the trip, the car travel through the city and has gas mileage that was six fewer miles per gallon in the gas mileage on the highway. If the total amount of got gasoline used for the trip was 9 gallons, find the gas mileage of the car on the highway.

Answer 1

x=mpg on the highway

x-6=mpg in the city

213-38=175 miles driven on the highway

(38/[x-6])+(175/x)=9

multiply both sides by the GCF (x^2-6x) of the denominators

after multiplying you get...

38x+175(x-6)=9(x^2-6x)

38x+175x-1050=9x^2-54x

213x-1050=9x^2-54x

9x^2-54x-213x+1050=0

9x^2-267x+1050=0

divide all terms by 3

3x^2-89x+350=0

factor

3*350=3*5*7*2*5=(3*5*5)*(2*7)=75*14 and 75+14=89, the coefficient of the middle term

(3x )(x )=0

the 3 must multiply the 25, so...

(3x )(x 25)=0

(3x 14)(x 25)=0

(3x-14)(x-25)=0

x-25=0

x=25 mpg highway

x-6=19 mpg city

check: 175/25=7 gallons of gas and 38/19=2 gallons of gas and 7+2=9