John and Ivory has some money each. If Ivory gives John $11, he will have 5 times as much money as her. If John gives Ivory $10, he will have the same amount of money as her. How much money does each person have respectively?

1. John?
2. Ivory?

	Case 1		Case 2
	John	Ivory	John	Ivory
Before	5 u - 11	1 u + 11	3 u + 10	3 u - 10
Change	+ 11	- 11	- 10	+ 10
After	5 u	1 u	3 u	3 u

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

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

Amount that John and Ivory each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that John has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 10
5 u - 3 u = 10 + 11

1 u = 21

Amount that John has
= 3 u + 10
= 3 x 21 + 10
= 63 + 10
= $73

(b)
Amount that Ivory has
= 1 u + 11
= 21 + 11
= $32

Answer(s): (a) $73; (b) $32