Y I have
£ 1. I spend 45p. How much do I have left?

55p

Step-by-step explanation:

£1 (100p) - 45p = 55p

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

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