If Usha gives Justin $29, the amount of money she has will be 30% of his. If Justin gives Usha $146, he will have the same amount of money as her. How much money did each of them have?
(a) Justin
(b) Usha

	Case 1		Case 2
	Justin	Usha	Justin	Usha
Before	10 u - 29	3 u + 29	6.5 u + 146	6.5 u - 146
Change	+ 29	- 29	- 146	+ 146
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

Amount that Usha 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 - 29 = 6.5 u + 146
10 u - 6.5 u = 146 + 29
3.5 u = 175 

1 u = 175 ÷ 3.5 = 50

Amount that Justin has
= 10 u - 29
= 10 x 50 - 29
= 500 - 29
= $471 

(b)
Amount that Usha has
= 3 u + 29
= 3 x 50 + 29
= 150 + 29
= $179

Answer(s): (a) $471; (b) $179