If Tammy gives Billy $39, the amount of money she has will be 40% of his. If Billy gives Tammy $27, he will have the same amount of money as her. How much money did each of them have?
(a) Billy
(b) Tammy

	Case 1		Case 2
	Billy	Tammy	Billy	Tammy
Before	5 u - 39	2 u + 39	3.5 u + 27	3.5 u - 27
Change	+ 39	- 39	- 27	+ 27
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 39 = 3.5 u + 27
5 u - 3.5 u = 27 + 39
1.5 u = 66 

1 u = 66 ÷ 1.5 = 44

Amount that Billy has
= 5 u - 39
= 5 x 44 - 39
= 220 - 39
= $181 

(b)
Amount that Tammy has
= 2 u + 39
= 2 x 44 + 39
= 88 + 39
= $127

Answer(s): (a) $181; (b) $127