Billy and Emma has some money each. If Emma gives Billy $11, he will have 3 times as much money as her. If Billy gives Emma $18, he will have the same amount of money as her. How much money does each person have respectively?

1. Billy?
2. Emma?

	Case 1		Case 2
	Billy	Emma	Billy	Emma
Before	3 u - 11	1 u + 11	2 u + 18	2 u - 18
Change	+ 11	- 11	- 18	+ 18
After	3 u	1 u	2 u	2 u

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

Total amount that Billy and Emma have in the end for both cases
= 3 u + 1 u
= 4 u

Amount that Billy and Emma each has in the end in Case 2
= 4 u ÷ 2
= 2 u

The amount that Billy has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 18
3 u - 2 u = 18 + 11

1 u = 29

Amount that Billy has
= 2 u + 18
= 2 x 29 + 18
= 58 + 18
= $76

(b)
Amount that Emma has
= 1 u + 11
= 29 + 11
= $40

Answer(s): (a) $76; (b) $40