If Jane gives Ivan $36, the amount of money she has will be 10% of his. If Ivan gives Jane $126, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Jane

	Case 1		Case 2
	Ivan	Jane	Ivan	Jane
Before	10 u - 36	1 u + 36	5.5 u + 126	5.5 u - 126
Change	+ 36	- 36	- 126	+ 126
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Ivan gives to Jane, there is an internal transfer of money from Ivan to Jane. 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 Jane and Ivan have
= 10 u + 1 u
= 11 u

Amount that Jane and Ivan each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 36 = 5.5 u + 126
10 u - 5.5 u = 126 + 36
4.5 u = 162 

1 u = 162 ÷ 4.5 = 36

Amount that Ivan has
= 10 u - 36
= 10 x 36 - 36
= 360 - 36
= $324 

(b)
Amount that Jane has
= 1 u + 36
= 1 x 36 + 36
= 36 + 36
= $72

Answer(s): (a) $324; (b) $72