If Abi gives Paul $32, the amount of money she has will be 25% of his. If Paul gives Abi $7, he will have the same amount of money as her. How much money did each of them have?
(a) Paul
(b) Abi

	Case 1		Case 2
	Paul	Abi	Paul	Abi
Before	4 u - 32	1 u + 32	2.5 u + 7	2.5 u - 7
Change	+ 32	- 32	- 7	+ 7
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

In Case 1, when Abi gives to Paul, there is an internal transfer of money from Abi to Paul.  The total amount that both have remains the same.

In Case 2, when Paul gives to Abi, there is an internal transfer of money from Paul to Abi. The total amount that both have remains the same.

The total amount that both have in Case 1 and Case 2 are the same.

Total amount that Abi and Paul have
= 4 u + 1 u
= 5 u

Amount that Abi and Paul each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

Amount that Paul has at first is the same in Case 1 and Case 2.

4 u - 32 = 2.5 u + 7
4 u - 2.5 u = 7 + 32
1.5 u = 39 

1 u = 39 ÷ 1.5 = 26

Amount that Paul has
= 4 u - 32
= 4 x 26 - 32
= 104 - 32
= $72 

(b)
Amount that Abi has
= 1 u + 32
= 1 x 26 + 32
= 26 + 32
= $58

Answer(s): (a) $72; (b) $58