If Vanessa gives Riordan $40, the amount of money she has will be 40% of his. If Riordan gives Vanessa $5, he will have the same amount of money as her. How much money did each of them have?
(a) Riordan
(b) Vanessa

	Case 1		Case 2
	Riordan	Vanessa	Riordan	Vanessa
Before	5 u - 40	2 u + 40	3.5 u + 5	3.5 u - 5
Change	+ 40	- 40	- 5	+ 5
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 40 = 3.5 u + 5
5 u - 3.5 u = 5 + 40
1.5 u = 45 

1 u = 45 ÷ 1.5 = 30

Amount that Riordan has
= 5 u - 40
= 5 x 30 - 40
= 150 - 40
= $110 

(b)
Amount that Vanessa has
= 2 u + 40
= 2 x 30 + 40
= 60 + 40
= $100

Answer(s): (a) $110; (b) $100