Patty buys a new car and gets it appraised every few years. After owning the car for 3 years, its value is $15,000. After owning the car for 5 years, its value is $9,000. If Patty gets her car appraised after owning it for 6 years, what will the car's value be in this indirect variation situation?

A. $7,500
B. $2,500
C. $6,000
D. $4,000

c) 6000

Step-by-step explanation:

the car's value would be $6000 because in two years the car decrased by $6000. Divide that by 2, and get $3000. That's how much it decreases in one year. $9000-$3000=$6000

btw I can't help it the car's original value was $24,000

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