If Lucy gives Tommy $18, the amount of money she has will be 30% of his. If Tommy gives Lucy $108, he will have the same amount of money as her. How much money did each of them have?
(a) Tommy
(b) Lucy

	Case 1		Case 2
	Tommy	Lucy	Tommy	Lucy
Before	10 u - 18	3 u + 18	6.5 u + 108	6.5 u - 108
Change	+ 18	- 18	- 108	+ 108
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Tommy gives to Lucy, there is an internal transfer of money from Tommy to Lucy. 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 Lucy and Tommy have
= 10 u + 3 u
= 13 u

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

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

10 u - 18 = 6.5 u + 108
10 u - 6.5 u = 108 + 18
3.5 u = 126 

1 u = 126 ÷ 3.5 = 36

Amount that Tommy has
= 10 u - 18
= 10 x 36 - 18
= 360 - 18
= $342 

(b)
Amount that Lucy has
= 3 u + 18
= 3 x 36 + 18
= 108 + 18
= $126

Answer(s): (a) $342; (b) $126