Charlie and Esther has some money each. If Esther gives Charlie $10, he will have 7 times as much money as her. If Charlie gives Esther $11, he will have the same amount of money as her. How much money does each person have respectively?

1. Charlie?
2. Esther?

	Case 1		Case 2
	Charlie	Esther	Charlie	Esther
Before	7 u - 10	1 u + 10	4 u + 11	4 u - 11
Change	+ 10	- 10	- 11	+ 11
After	7 u	1 u	4 u	4 u

(a)
If Esther gives Charlie some money or Charlie gives Esther some money, the total amount of money remains the same.  

Total amount that Charlie and Esther have in the end for both cases
= 7 u + 1 u
= 8 u

Amount that Charlie and Esther each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Charlie has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 11
7 u - 4 u = 11 + 10

1 u = 21

Amount that Charlie has
= 4 u + 11
= 4 x 21 + 11
= 84 + 11
= $95

(b)
Amount that Esther has
= 1 u + 10
= 21 + 10
= $31

Answer(s): (a) $95; (b) $31