If Emma gives Vincent $16, the amount of money she has will be 30% of his. If Vincent gives Emma $145, he will have the same amount of money as her. How much money did each of them have?
(a) Vincent
(b) Emma

	Case 1		Case 2
	Vincent	Emma	Vincent	Emma
Before	10 u - 16	3 u + 16	6.5 u + 145	6.5 u - 145
Change	+ 16	- 16	- 145	+ 145
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 16 = 6.5 u + 145
10 u - 6.5 u = 145 + 16
3.5 u = 161 

1 u = 161 ÷ 3.5 = 46

Amount that Vincent has
= 10 u - 16
= 10 x 46 - 16
= 460 - 16
= $444 

(b)
Amount that Emma has
= 3 u + 16
= 3 x 46 + 16
= 138 + 16
= $154

Answer(s): (a) $444; (b) $154