If Gwen gives Oliver $27, the amount of money she has will be 30% of his. If Oliver gives Gwen $120, he will have the same amount of money as her. How much money did each of them have?
(a) Oliver
(b) Gwen

	Case 1		Case 2
	Oliver	Gwen	Oliver	Gwen
Before	10 u - 27	3 u + 27	6.5 u + 120	6.5 u - 120
Change	+ 27	- 27	- 120	+ 120
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Oliver gives to Gwen, there is an internal transfer of money from Oliver 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 Oliver have
= 10 u + 3 u
= 13 u

Amount that Gwen and Oliver each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 27 = 6.5 u + 120
10 u - 6.5 u = 120 + 27
3.5 u = 147 

1 u = 147 ÷ 3.5 = 42

Amount that Oliver has
= 10 u - 27
= 10 x 42 - 27
= 420 - 27
= $393 

(b)
Amount that Gwen has
= 3 u + 27
= 3 x 42 + 27
= 126 + 27
= $153

Answer(s): (a) $393; (b) $153