Mike and Molly share some money in the ratio 2 : 3. Molly gets 135 AED more than Mike.

(b) How much do they each get?

Mike 270

Molly 405

Step-by-step explanation:

Let Mike be x

Let Molly be x + 135

2/3 = x/(x + 135)                        Cross Multiply

2*(x + 135) = 3x                         Remove the brackets

2x + 270 = 3x                            Subtract 2x from both sides

2x-2x + 270 = 3x - 2x

270 = x

Mike gets 270

Molly gets 270 + 135

Molly gets 405

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