If Hazel gives Vincent $38, the amount of money she has will be 40% of his. If Vincent gives Hazel $16, he will have the same amount of money as her. How much money did each of them have?
(a) Vincent
(b) Hazel

	Case 1		Case 2
	Vincent	Hazel	Vincent	Hazel
Before	5 u - 38	2 u + 38	3.5 u + 16	3.5 u - 16
Change	+ 38	- 38	- 16	+ 16
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 38 = 3.5 u + 16
5 u - 3.5 u = 16 + 38
1.5 u = 54 

1 u = 54 ÷ 1.5 = 36

Amount that Vincent has
= 5 u - 38
= 5 x 36 - 38
= 180 - 38
= $142 

(b)
Amount that Hazel has
= 2 u + 38
= 2 x 36 + 38
= 72 + 38
= $110

Answer(s): (a) $142; (b) $110