A counselor surveys a random sample of 60 out of 900 high school students. 75% of them said they were going to college. She used these results to determine that 675 students in the overall school would be planning to go to college. Do you agree with her prediction?

y=mx+

one that is bigger than 3 1/2

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