If Nicole gives Ivan $20, the amount of money she has will be 25% of his. If Ivan gives Nicole $19, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Nicole

	Case 1		Case 2
	Ivan	Nicole	Ivan	Nicole
Before	4 u - 20	1 u + 20	2.5 u + 19	2.5 u - 19
Change	+ 20	- 20	- 19	+ 19
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

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

Amount that Nicole 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 - 20 = 2.5 u + 19
4 u - 2.5 u = 19 + 20
1.5 u = 39 

1 u = 39 ÷ 1.5 = 26

Amount that Ivan has
= 4 u - 20
= 4 x 26 - 20
= 104 - 20
= $84 

(b)
Amount that Nicole has
= 1 u + 20
= 1 x 26 + 20
= 26 + 20
= $46

Answer(s): (a) $84; (b) $46