If Victoria gives Tommy $17, the amount of money she has will be 40% of his. If Tommy gives Victoria $46, he will have the same amount of money as her. How much money did each of them have?
(a) Tommy
(b) Victoria

	Case 1		Case 2
	Tommy	Victoria	Tommy	Victoria
Before	5 u - 17	2 u + 17	3.5 u + 46	3.5 u - 46
Change	+ 17	- 17	- 46	+ 46
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 17 = 3.5 u + 46
5 u - 3.5 u = 46 + 17
1.5 u = 63 

1 u = 63 ÷ 1.5 = 42

Amount that Tommy has
= 5 u - 17
= 5 x 42 - 17
= 210 - 17
= $193 

(b)
Amount that Victoria has
= 2 u + 17
= 2 x 42 + 17
= 84 + 17
= $101

Answer(s): (a) $193; (b) $101