If Irene gives Billy $32, the amount of money she has will be 30% of his. If Billy gives Irene $52, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Irene

	Case 1		Case 2
	Billy	Irene	Billy	Irene
Before	10 u - 32	3 u + 32	6.5 u + 52	6.5 u - 52
Change	+ 32	- 32	- 52	+ 52
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 32 = 6.5 u + 52
10 u - 6.5 u = 52 + 32
3.5 u = 84 

1 u = 84 ÷ 3.5 = 24

Amount that Billy has
= 10 u - 32
= 10 x 24 - 32
= 240 - 32
= $208 

(b)
Amount that Irene has
= 3 u + 32
= 3 x 24 + 32
= 72 + 32
= $104

Answer(s): (a) $208; (b) $104