If Cathy gives Ben $38, the amount of money she has will be 25% of his. If Ben gives Cathy $34, he will have the same amount of money as her. How much money did each of them have?
(a) Ben
(b) Cathy

	Case 1		Case 2
	Ben	Cathy	Ben	Cathy
Before	4 u - 38	1 u + 38	2.5 u + 34	2.5 u - 34
Change	+ 38	- 38	- 34	+ 34
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Ben gives to Cathy, there is an internal transfer of money from Ben to Cathy. 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 Cathy and Ben have
= 4 u + 1 u
= 5 u

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

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

4 u - 38 = 2.5 u + 34
4 u - 2.5 u = 34 + 38
1.5 u = 72 

1 u = 72 ÷ 1.5 = 48

Amount that Ben has
= 4 u - 38
= 4 x 48 - 38
= 192 - 38
= $154 

(b)
Amount that Cathy has
= 1 u + 38
= 1 x 48 + 38
= 48 + 38
= $86

Answer(s): (a) $154; (b) $86