If Kathy gives Ahmad $34, the amount of money she has will be 30% of his. If Ahmad gives Kathy $127, he will have the same amount of money as her. How much money did each of them have?
(a) Ahmad
(b) Kathy

	Case 1		Case 2
	Ahmad	Kathy	Ahmad	Kathy
Before	10 u - 34	3 u + 34	6.5 u + 127	6.5 u - 127
Change	+ 34	- 34	- 127	+ 127
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Ahmad gives to Kathy, there is an internal transfer of money from Ahmad 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 Ahmad have
= 10 u + 3 u
= 13 u

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

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

10 u - 34 = 6.5 u + 127
10 u - 6.5 u = 127 + 34
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Ahmad has
= 10 u - 34
= 10 x 46 - 34
= 460 - 34
= $426 

(b)
Amount that Kathy has
= 3 u + 34
= 3 x 46 + 34
= 138 + 34
= $172

Answer(s): (a) $426; (b) $172