If Tina gives Rael $21, the amount of money she has will be 25% of his. If Rael gives Tina $27, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Tina

	Case 1		Case 2
	Rael	Tina	Rael	Tina
Before	4 u - 21	1 u + 21	2.5 u + 27	2.5 u - 27
Change	+ 21	- 21	- 27	+ 27
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 21 = 2.5 u + 27
4 u - 2.5 u = 27 + 21
1.5 u = 48 

1 u = 48 ÷ 1.5 = 32

Amount that Rael has
= 4 u - 21
= 4 x 32 - 21
= 128 - 21
= $107 

(b)
Amount that Tina has
= 1 u + 21
= 1 x 32 + 21
= 32 + 21
= $53

Answer(s): (a) $107; (b) $53