Caroline, Colin & Sarah share some money.
Caroline gets of the money.
Colin and Sarah share the rest in the ratio 3:1.
"What proportion does Colin get?

Colin gets  

Step-by-step explanation:

One part is excluded in the problem. That part is:

"Caroline gets of the money."

Solution:

If Caroline gets 1/9th, then remaining is:

Colin and Sarah share in ratio 3 is to 1, that means 3 + 1 = 4 parts...

8/9th in 4 parts means, each part is:

We know Colin gets "3" parts of the total, each part is (2/9)th, so 3 parts would be:

Colin gets  

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