If Jean gives Justin $30, the amount of money she has will be 30% of his. If Justin gives Jean $89, he will have the same amount of money as her. How much money did each of them have?
(a) Justin
(b) Jean

	Case 1		Case 2
	Justin	Jean	Justin	Jean
Before	10 u - 30	3 u + 30	6.5 u + 89	6.5 u - 89
Change	+ 30	- 30	- 89	+ 89
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Justin gives to Jean, there is an internal transfer of money from Justin to Jean. 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 Jean and Justin have
= 10 u + 3 u
= 13 u

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

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

10 u - 30 = 6.5 u + 89
10 u - 6.5 u = 89 + 30
3.5 u = 119 

1 u = 119 ÷ 3.5 = 34

Amount that Justin has
= 10 u - 30
= 10 x 34 - 30
= 340 - 30
= $310 

(b)
Amount that Jean has
= 3 u + 30
= 3 x 34 + 30
= 102 + 30
= $132

Answer(s): (a) $310; (b) $132