This year, Martin’s income is 1/4 greater than his income from last year. If s represents his income from last year, what is his income this year? a) 1/4s

b) 4/5s

c) 5/4s

d) 4s

∠cbe and ∠deb are same-side interior angles.

i took the test

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

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0