Sean and Diana has some money each. If Diana gives Sean $20, he will have 5 times as much money as her. If Sean gives Diana $13, he will have the same amount of money as her. How much money does each person have respectively?

1. Sean?
2. Diana?

	Case 1		Case 2
	Sean	Diana	Sean	Diana
Before	5 u - 20	1 u + 20	3 u + 13	3 u - 13
Change	+ 20	- 20	- 13	+ 13
After	5 u	1 u	3 u	3 u

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

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

Amount that Sean and Diana each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Sean has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 13
5 u - 3 u = 13 + 20

1 u = 33

Amount that Sean has
= 3 u + 13
= 3 x 33 + 13
= 99 + 13
= $112

(b)
Amount that Diana has
= 1 u + 20
= 33 + 20
= $53

Answer(s): (a) $112; (b) $53