7. A liquid starts at a temperature of 65 degrees and its temperature increases by a rate of 5 degrees per minute. How many minutes will it take for the temperature of the liquid to reach
128 degrees?

the correct answer is 5 6 and 7

30005

yes ok                                            

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