If Zara gives Rael $21, the amount of money she has will be 40% of his. If Rael gives Zara $30, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Zara

	Case 1		Case 2
	Rael	Zara	Rael	Zara
Before	5 u - 21	2 u + 21	3.5 u + 30	3.5 u - 30
Change	+ 21	- 21	- 30	+ 30
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Rael gives to Zara, there is an internal transfer of money from Rael to Zara. 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 Zara and Rael have
= 5 u + 2 u
= 7 u

Amount that Zara and Rael each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 21 = 3.5 u + 30
5 u - 3.5 u = 30 + 21
1.5 u = 51 

1 u = 51 ÷ 1.5 = 34

Amount that Rael has
= 5 u - 21
= 5 x 34 - 21
= 170 - 21
= $149 

(b)
Amount that Zara has
= 2 u + 21
= 2 x 34 + 21
= 68 + 21
= $89

Answer(s): (a) $149; (b) $89