If Linda gives Pierre $19, the amount of money she has will be 10% of his. If Pierre gives Linda $116, he will have the same amount of money as her. How much money did each of them have?
(a) Pierre
(b) Linda

	Case 1		Case 2
	Pierre	Linda	Pierre	Linda
Before	10 u - 19	1 u + 19	5.5 u + 116	5.5 u - 116
Change	+ 19	- 19	- 116	+ 116
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Pierre gives to Linda, there is an internal transfer of money from Pierre to Linda. 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 Linda and Pierre have
= 10 u + 1 u
= 11 u

Amount that Linda and Pierre each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 19 = 5.5 u + 116
10 u - 5.5 u = 116 + 19
4.5 u = 135 

1 u = 135 ÷ 4.5 = 30

Amount that Pierre has
= 10 u - 19
= 10 x 30 - 19
= 300 - 19
= $281 

(b)
Amount that Linda has
= 1 u + 19
= 1 x 30 + 19
= 30 + 19
= $49

Answer(s): (a) $281; (b) $49