If Olivia gives Pierre $14, the amount of money she has will be 40% of his. If Pierre gives Olivia $58, he will have the same amount of money as her. How much money did each of them have?
(a) Pierre
(b) Olivia

	Case 1		Case 2
	Pierre	Olivia	Pierre	Olivia
Before	5 u - 14	2 u + 14	3.5 u + 58	3.5 u - 58
Change	+ 14	- 14	- 58	+ 58
After	5 u	2 u	3.5 u	3.5 u

(a)
40% = ⁴⁰₁₀₀ = ²₅

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

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

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

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

5 u - 14 = 3.5 u + 58
5 u - 3.5 u = 58 + 14
1.5 u = 72 

1 u = 72 ÷ 1.5 = 48

Amount that Pierre has
= 5 u - 14
= 5 x 48 - 14
= 240 - 14
= $226 

(b)
Amount that Olivia has
= 2 u + 14
= 2 x 48 + 14
= 96 + 14
= $110

Answer(s): (a) $226; (b) $110