If Zoe gives Ivan $26, the amount of money she has will be 25% of his. If Ivan gives Zoe $49, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Zoe

	Case 1		Case 2
	Ivan	Zoe	Ivan	Zoe
Before	4 u - 26	1 u + 26	2.5 u + 49	2.5 u - 49
Change	+ 26	- 26	- 49	+ 49
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

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

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

4 u - 26 = 2.5 u + 49
4 u - 2.5 u = 49 + 26
1.5 u = 75 

1 u = 75 ÷ 1.5 = 50

Amount that Ivan has
= 4 u - 26
= 4 x 50 - 26
= 200 - 26
= $174 

(b)
Amount that Zoe has
= 1 u + 26
= 1 x 50 + 26
= 50 + 26
= $76

Answer(s): (a) $174; (b) $76