If Jane gives Billy $15, the amount of money she has will be 40% of his. If Billy gives Jane $15, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Jane

	Case 1		Case 2
	Billy	Jane	Billy	Jane
Before	5 u - 15	2 u + 15	3.5 u + 15	3.5 u - 15
Change	+ 15	- 15	- 15	+ 15
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 15 = 3.5 u + 15
5 u - 3.5 u = 15 + 15
1.5 u = 30 

1 u = 30 ÷ 1.5 = 20

Amount that Billy has
= 5 u - 15
= 5 x 20 - 15
= 100 - 15
= $85 

(b)
Amount that Jane has
= 2 u + 15
= 2 x 20 + 15
= 40 + 15
= $55

Answer(s): (a) $85; (b) $55