If Emily gives Oliver $19, the amount of money she has will be 40% of his. If Oliver gives Emily $53, he will have the same amount of money as her. How much money did each of them have?
(a) Oliver
(b) Emily

	Case 1		Case 2
	Oliver	Emily	Oliver	Emily
Before	5 u - 19	2 u + 19	3.5 u + 53	3.5 u - 53
Change	+ 19	- 19	- 53	+ 53
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

In Case 2, when Oliver gives to Emily, there is an internal transfer of money from Oliver 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 Oliver have
= 5 u + 2 u
= 7 u

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

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

5 u - 19 = 3.5 u + 53
5 u - 3.5 u = 53 + 19
1.5 u = 72 

1 u = 72 ÷ 1.5 = 48

Amount that Oliver has
= 5 u - 19
= 5 x 48 - 19
= 240 - 19
= $221 

(b)
Amount that Emily has
= 2 u + 19
= 2 x 48 + 19
= 96 + 19
= $115

Answer(s): (a) $221; (b) $115