Peter and Emma has some money each. If Emma gives Peter $10, he will have 3 times as much money as her. If Peter gives Emma $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Peter?
2. Emma?

	Case 1		Case 2
	Peter	Emma	Peter	Emma
Before	3 u - 10	1 u + 10	2 u + 19	2 u - 19
Change	+ 10	- 10	- 19	+ 19
After	3 u	1 u	2 u	2 u

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

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

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

The amount that Peter has at first in Case 1 and Case 2 is the same.
3 u - 10 = 2 u + 19
3 u - 2 u = 19 + 10

1 u = 29

Amount that Peter has
= 2 u + 19
= 2 x 29 + 19
= 58 + 19
= $77

(b)
Amount that Emma has
= 1 u + 10
= 29 + 10
= $39

Answer(s): (a) $77; (b) $39