Mark partially drained his pool to clean it. at 1: 00 p. m., he started to refill it. at 5: 00 p. m., the pool had 10,400 gallons of water. at 9: 00 p. m., the pool had 13,800 gallons of water. if filling the pool is modeled by a linear function, how many gallons of water still remained in the pool when he first started to refill it?

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1

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