If Betty gives Billy $18, the amount of money she has will be 25% of his. If Billy gives Betty $33, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Betty

	Case 1		Case 2
	Billy	Betty	Billy	Betty
Before	4 u - 18	1 u + 18	2.5 u + 33	2.5 u - 33
Change	+ 18	- 18	- 33	+ 33
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Billy gives to Betty, there is an internal transfer of money from Billy to Betty. 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 Betty and Billy have
= 4 u + 1 u
= 5 u

Amount that Betty and Billy each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 18 = 2.5 u + 33
4 u - 2.5 u = 33 + 18
1.5 u = 51 

1 u = 51 ÷ 1.5 = 34

Amount that Billy has
= 4 u - 18
= 4 x 34 - 18
= 136 - 18
= $118 

(b)
Amount that Betty has
= 1 u + 18
= 1 x 34 + 18
= 34 + 18
= $52

Answer(s): (a) $118; (b) $52