If Kathy gives Oscar $29, the amount of money she has will be 10% of his. If Oscar gives Kathy $88, he will have the same amount of money as her. How much money did each of them have?
(a) Oscar
(b) Kathy

	Case 1		Case 2
	Oscar	Kathy	Oscar	Kathy
Before	10 u - 29	1 u + 29	5.5 u + 88	5.5 u - 88
Change	+ 29	- 29	- 88	+ 88
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 29 = 5.5 u + 88
10 u - 5.5 u = 88 + 29
4.5 u = 117 

1 u = 117 ÷ 4.5 = 26

Amount that Oscar has
= 10 u - 29
= 10 x 26 - 29
= 260 - 29
= $231 

(b)
Amount that Kathy has
= 1 u + 29
= 1 x 26 + 29
= 26 + 29
= $55

Answer(s): (a) $231; (b) $55