If Gwen gives Will $27, the amount of money she has will be 40% of his. If Will gives Gwen $3, he will have the same amount of money as her. How much money did each of them have?
(a) Will
(b) Gwen

	Case 1		Case 2
	Will	Gwen	Will	Gwen
Before	5 u - 27	2 u + 27	3.5 u + 3	3.5 u - 3
Change	+ 27	- 27	- 3	+ 3
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 27 = 3.5 u + 3
5 u - 3.5 u = 3 + 27
1.5 u = 30 

1 u = 30 ÷ 1.5 = 20

Amount that Will has
= 5 u - 27
= 5 x 20 - 27
= 100 - 27
= $73 

(b)
Amount that Gwen has
= 2 u + 27
= 2 x 20 + 27
= 40 + 27
= $67

Answer(s): (a) $73; (b) $67