If Rachel gives Bryan $17, the amount of money she has will be 40% of his. If Bryan gives Rachel $49, he will have the same amount of money as her. How much money did each of them have?
(a) Bryan
(b) Rachel

	Case 1		Case 2
	Bryan	Rachel	Bryan	Rachel
Before	5 u - 17	2 u + 17	3.5 u + 49	3.5 u - 49
Change	+ 17	- 17	- 49	+ 49
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Bryan gives to Rachel, there is an internal transfer of money from Bryan to Rachel. 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 Rachel and Bryan have
= 5 u + 2 u
= 7 u

Amount that Rachel and Bryan each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u

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

5 u - 17 = 3.5 u + 49
5 u - 3.5 u = 49 + 17
1.5 u = 66 

1 u = 66 ÷ 1.5 = 44

Amount that Bryan has
= 5 u - 17
= 5 x 44 - 17
= 220 - 17
= $203 

(b)
Amount that Rachel has
= 2 u + 17
= 2 x 44 + 17
= 88 + 17
= $105

Answer(s): (a) $203; (b) $105