Peter and Kathy has some money each. If Kathy gives Peter $13, he will have 5 times as much money as her. If Peter gives Kathy $18, he will have the same amount of money as her. How much money does each person have respectively?

1. Peter?
2. Kathy?

	Case 1		Case 2
	Peter	Kathy	Peter	Kathy
Before	5 u - 13	1 u + 13	3 u + 18	3 u - 18
Change	+ 13	- 13	- 18	+ 18
After	5 u	1 u	3 u	3 u

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

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

Amount that Peter and Kathy each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Peter has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 18
5 u - 3 u = 18 + 13

1 u = 31

Amount that Peter has
= 3 u + 18
= 3 x 31 + 18
= 93 + 18
= $111

(b)
Amount that Kathy has
= 1 u + 13
= 31 + 13
= $44

Answer(s): (a) $111; (b) $44