14. When Mischa filled her car's gas tank before beginning a trip, the car's odometer read 44,587 miles. When she stopped for
her
gas next, she filled her tank back up with 17 gallons. She noticed that
new odometer reading was 44,895 miles. How many miles per gallon was she getting on the
first leg of her trip?

Step-by-step explanation:

44,895-44,587 = 308 total gallons

308/17 = 18.12

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

step-by-step explanation: