If Rachel gives Jack $36, the amount of money she has will be 30% of his. If Jack gives Rachel $125, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Rachel

	Case 1		Case 2
	Jack	Rachel	Jack	Rachel
Before	10 u - 36	3 u + 36	6.5 u + 125	6.5 u - 125
Change	+ 36	- 36	- 125	+ 125
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 36 = 6.5 u + 125
10 u - 6.5 u = 125 + 36
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Jack has
= 10 u - 36
= 10 x 46 - 36
= 460 - 36
= $424 

(b)
Amount that Rachel has
= 3 u + 36
= 3 x 46 + 36
= 138 + 36
= $174

Answer(s): (a) $424; (b) $174