If Wendy gives Tommy $33, the amount of money she has will be 10% of his. If Tommy gives Wendy $138, he will have the same amount of money as her. How much money did each of them have?
(a) Tommy
(b) Wendy

	Case 1		Case 2
	Tommy	Wendy	Tommy	Wendy
Before	10 u - 33	1 u + 33	5.5 u + 138	5.5 u - 138
Change	+ 33	- 33	- 138	+ 138
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Tommy gives to Wendy, there is an internal transfer of money from Tommy to Wendy. 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 Wendy and Tommy have
= 10 u + 1 u
= 11 u

Amount that Wendy and Tommy each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 33 = 5.5 u + 138
10 u - 5.5 u = 138 + 33
4.5 u = 171 

1 u = 171 ÷ 4.5 = 38

Amount that Tommy has
= 10 u - 33
= 10 x 38 - 33
= 380 - 33
= $347 

(b)
Amount that Wendy has
= 1 u + 33
= 1 x 38 + 33
= 38 + 33
= $71

Answer(s): (a) $347; (b) $71