If Jean gives Howard $32, the amount of money she has will be 40% of his. If Howard gives Jean $28, he will have the same amount of money as her. How much money did each of them have?
(a) Howard
(b) Jean

	Case 1		Case 2
	Howard	Jean	Howard	Jean
Before	5 u - 32	2 u + 32	3.5 u + 28	3.5 u - 28
Change	+ 32	- 32	- 28	+ 28
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Howard gives to Jean, there is an internal transfer of money from Howard 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 Howard have
= 5 u + 2 u
= 7 u

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

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

5 u - 32 = 3.5 u + 28
5 u - 3.5 u = 28 + 32
1.5 u = 60 

1 u = 60 ÷ 1.5 = 40

Amount that Howard has
= 5 u - 32
= 5 x 40 - 32
= 200 - 32
= $168 

(b)
Amount that Jean has
= 2 u + 32
= 2 x 40 + 32
= 80 + 32
= $112

Answer(s): (a) $168; (b) $112