If Cindy gives Bobby $24, the amount of money she has will be 40% of his. If Bobby gives Cindy $33, he will have the same amount of money as her. How much money did each of them have?
(a) Bobby
(b) Cindy

	Case 1		Case 2
	Bobby	Cindy	Bobby	Cindy
Before	5 u - 24	2 u + 24	3.5 u + 33	3.5 u - 33
Change	+ 24	- 24	- 33	+ 33
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 24 = 3.5 u + 33
5 u - 3.5 u = 33 + 24
1.5 u = 57 

1 u = 57 ÷ 1.5 = 38

Amount that Bobby has
= 5 u - 24
= 5 x 38 - 24
= 190 - 24
= $166 

(b)
Amount that Cindy has
= 2 u + 24
= 2 x 38 + 24
= 76 + 24
= $100

Answer(s): (a) $166; (b) $100