If Hilda gives Ahmad $22, the amount of money she has will be 25% of his. If Ahmad gives Hilda $44, he will have the same amount of money as her. How much money did each of them have?
(a) Ahmad
(b) Hilda

	Case 1		Case 2
	Ahmad	Hilda	Ahmad	Hilda
Before	4 u - 22	1 u + 22	2.5 u + 44	2.5 u - 44
Change	+ 22	- 22	- 44	+ 44
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Ahmad gives to Hilda, there is an internal transfer of money from Ahmad to Hilda. 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 Hilda and Ahmad have
= 4 u + 1 u
= 5 u

Amount that Hilda and Ahmad each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 22 = 2.5 u + 44
4 u - 2.5 u = 44 + 22
1.5 u = 66 

1 u = 66 ÷ 1.5 = 44

Amount that Ahmad has
= 4 u - 22
= 4 x 44 - 22
= 176 - 22
= $154 

(b)
Amount that Hilda has
= 1 u + 22
= 1 x 44 + 22
= 44 + 22
= $66

Answer(s): (a) $154; (b) $66