If Emma gives Jack $14, the amount of money she has will be 40% of his. If Jack gives Emma $40, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Emma

	Case 1		Case 2
	Jack	Emma	Jack	Emma
Before	5 u - 14	2 u + 14	3.5 u + 40	3.5 u - 40
Change	+ 14	- 14	- 40	+ 40
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 14 = 3.5 u + 40
5 u - 3.5 u = 40 + 14
1.5 u = 54 

1 u = 54 ÷ 1.5 = 36

Amount that Jack has
= 5 u - 14
= 5 x 36 - 14
= 180 - 14
= $166 

(b)
Amount that Emma has
= 2 u + 14
= 2 x 36 + 14
= 72 + 14
= $86

Answer(s): (a) $166; (b) $86