If Emily gives Tom $19, the amount of money she has will be 25% of his. If Tom gives Emily $14, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Emily

	Case 1		Case 2
	Tom	Emily	Tom	Emily
Before	4 u - 19	1 u + 19	2.5 u + 14	2.5 u - 14
Change	+ 19	- 19	- 14	+ 14
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Tom gives to Emily, there is an internal transfer of money from Tom to Emily. 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 Emily and Tom have
= 4 u + 1 u
= 5 u

Amount that Emily and Tom each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 19 = 2.5 u + 14
4 u - 2.5 u = 14 + 19
1.5 u = 33 

1 u = 33 ÷ 1.5 = 22

Amount that Tom has
= 4 u - 19
= 4 x 22 - 19
= 88 - 19
= $69 

(b)
Amount that Emily has
= 1 u + 19
= 1 x 22 + 19
= 22 + 19
= $41

Answer(s): (a) $69; (b) $41