If Erika gives Ian $38, the amount of money she has will be 30% of his. If Ian gives Erika $123, he will have the same amount of money as her. How much money did each of them have?
(a) Ian
(b) Erika

	Case 1		Case 2
	Ian	Erika	Ian	Erika
Before	10 u - 38	3 u + 38	6.5 u + 123	6.5 u - 123
Change	+ 38	- 38	- 123	+ 123
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Ian gives to Erika, there is an internal transfer of money from Ian to Erika. 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 Erika and Ian have
= 10 u + 3 u
= 13 u

Amount that Erika and Ian each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 38 = 6.5 u + 123
10 u - 6.5 u = 123 + 38
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Ian has
= 10 u - 38
= 10 x 46 - 38
= 460 - 38
= $422 

(b)
Amount that Erika has
= 3 u + 38
= 3 x 46 + 38
= 138 + 38
= $176

Answer(s): (a) $422; (b) $176