If Abi gives Sean $38, the amount of money she has will be 10% of his. If Sean gives Abi $61, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Abi

	Case 1		Case 2
	Sean	Abi	Sean	Abi
Before	10 u - 38	1 u + 38	5.5 u + 61	5.5 u - 61
Change	+ 38	- 38	- 61	+ 61
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 38 = 5.5 u + 61
10 u - 5.5 u = 61 + 38
4.5 u = 99 

1 u = 99 ÷ 4.5 = 22

Amount that Sean has
= 10 u - 38
= 10 x 22 - 38
= 220 - 38
= $182 

(b)
Amount that Abi has
= 1 u + 38
= 1 x 22 + 38
= 22 + 38
= $60

Answer(s): (a) $182; (b) $60