If Anna gives Ivan $27, the amount of money she has will be 10% of his. If Ivan gives Anna $171, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Anna

	Case 1		Case 2
	Ivan	Anna	Ivan	Anna
Before	10 u - 27	1 u + 27	5.5 u + 171	5.5 u - 171
Change	+ 27	- 27	- 171	+ 171
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Anna 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 - 27 = 5.5 u + 171
10 u - 5.5 u = 171 + 27
4.5 u = 198 

1 u = 198 ÷ 4.5 = 44

Amount that Ivan has
= 10 u - 27
= 10 x 44 - 27
= 440 - 27
= $413 

(b)
Amount that Anna has
= 1 u + 27
= 1 x 44 + 27
= 44 + 27
= $71

Answer(s): (a) $413; (b) $71