If Cathy gives Warren $27, the amount of money she has will be 25% of his. If Warren gives Cathy $30, he will have the same amount of money as her. How much money did each of them have?
(a) Warren
(b) Cathy

	Case 1		Case 2
	Warren	Cathy	Warren	Cathy
Before	4 u - 27	1 u + 27	2.5 u + 30	2.5 u - 30
Change	+ 27	- 27	- 30	+ 30
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 27 = 2.5 u + 30
4 u - 2.5 u = 30 + 27
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Warren has
= 4 u - 27
= 4 x 38 - 27
= 152 - 27
= $125 

(b)
Amount that Cathy has
= 1 u + 27
= 1 x 38 + 27
= 38 + 27
= $65

Answer(s): (a) $125; (b) $65