If Gwen gives Paul $22, the amount of money she has will be 30% of his. If Paul gives Gwen $69, he will have the same amount of money as her. How much money did each of them have?
(a) Paul
(b) Gwen

	Case 1		Case 2
	Paul	Gwen	Paul	Gwen
Before	10 u - 22	3 u + 22	6.5 u + 69	6.5 u - 69
Change	+ 22	- 22	- 69	+ 69
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Paul gives to Gwen, there is an internal transfer of money from Paul to Gwen. 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 Gwen and Paul have
= 10 u + 3 u
= 13 u

Amount that Gwen and Paul each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 22 = 6.5 u + 69
10 u - 6.5 u = 69 + 22
3.5 u = 91 

1 u = 91 ÷ 3.5 = 26

Amount that Paul has
= 10 u - 22
= 10 x 26 - 22
= 260 - 22
= $238 

(b)
Amount that Gwen has
= 3 u + 22
= 3 x 26 + 22
= 78 + 22
= $100

Answer(s): (a) $238; (b) $100