Clint completely filled his 18-gallon tank of gas with regular fuel for $55.08. As he left the gas station, he noticed the station across the street sold regular fuel priced at $2.99 per gallon. How much money could Clint have saved per gallon if he had gone to the station across the street?

step-by-step explanation:

de-gf

hj=3x+20

ji=15x-64

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4