If Sarah gives Ian $28, the amount of money she has will be 30% of his. If Ian gives Sarah $56, he will have the same amount of money as her. How much money did each of them have?
(a) Ian
(b) Sarah

	Case 1		Case 2
	Ian	Sarah	Ian	Sarah
Before	10 u - 28	3 u + 28	6.5 u + 56	6.5 u - 56
Change	+ 28	- 28	- 56	+ 56
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Sarah 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 - 28 = 6.5 u + 56
10 u - 6.5 u = 56 + 28
3.5 u = 84 

1 u = 84 ÷ 3.5 = 24

Amount that Ian has
= 10 u - 28
= 10 x 24 - 28
= 240 - 28
= $212 

(b)
Amount that Sarah has
= 3 u + 28
= 3 x 24 + 28
= 72 + 28
= $100

Answer(s): (a) $212; (b) $100