If Raeann gives Peter $21, the amount of money she has will be 25% of his. If Peter gives Raeann $39, he will have the same amount of money as her. How much money did each of them have?
(a) Peter
(b) Raeann

	Case 1		Case 2
	Peter	Raeann	Peter	Raeann
Before	4 u - 21	1 u + 21	2.5 u + 39	2.5 u - 39
Change	+ 21	- 21	- 39	+ 39
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 21 = 2.5 u + 39
4 u - 2.5 u = 39 + 21
1.5 u = 60 

1 u = 60 ÷ 1.5 = 40

Amount that Peter has
= 4 u - 21
= 4 x 40 - 21
= 160 - 21
= $139 

(b)
Amount that Raeann has
= 1 u + 21
= 1 x 40 + 21
= 40 + 21
= $61

Answer(s): (a) $139; (b) $61