If Raeann gives Ivan $15, the amount of money she has will be 75% of his. If Ivan gives Raeann $8, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Raeann

	Case 1		Case 2
	Ivan	Raeann	Ivan	Raeann
Before	4 u - 15	3 u + 15	3.5 u + 8	3.5 u - 8
Change	+ 15	- 15	- 8	+ 8
After	4 u	3 u	3.5 u	3.5 u

(a)
75% = ⁷⁵₁₀₀ = ³₄

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

In Case 2, when Ivan gives to Raeann, there is an internal transfer of money from Ivan 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 Ivan have
= 4 u + 3 u
= 7 u

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

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

4 u - 15 = 3.5 u + 8
4 u - 3.5 u = 8 + 15
0.5 u = 23 

1 u = 23 ÷ 0.5 = 46

Amount that Ivan has
= 4 u - 15
= 4 x 46 - 15
= 184 - 15
= $169 

(b)
Amount that Raeann has
= 3 u + 15
= 3 x 46 + 15
= 138 + 15
= $153

Answer(s): (a) $169; (b) $153