Bobby and Esther has some money each. If Esther gives Bobby $11, he will have 5 times as much money as her. If Bobby gives Esther $15, he will have the same amount of money as her. How much money does each person have respectively?

1. Bobby?
2. Esther?

	Case 1		Case 2
	Bobby	Esther	Bobby	Esther
Before	5 u - 11	1 u + 11	3 u + 15	3 u - 15
Change	+ 11	- 11	- 15	+ 15
After	5 u	1 u	3 u	3 u

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

Total amount that Bobby and Esther have in the end for both cases
= 5 u + 1 u
= 6 u

Amount that Bobby and Esther each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Bobby has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 15
5 u - 3 u = 15 + 11

1 u = 26

Amount that Bobby has
= 3 u + 15
= 3 x 26 + 15
= 78 + 15
= $93

(b)
Amount that Esther has
= 1 u + 11
= 26 + 11
= $37

Answer(s): (a) $93; (b) $37