Tommy and Diana has some money each. If Diana gives Tommy $10, he will have 7 times as much money as her. If Tommy gives Diana $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Tommy?
2. Diana?

	Case 1		Case 2
	Tommy	Diana	Tommy	Diana
Before	7 u - 10	1 u + 10	4 u + 19	4 u - 19
Change	+ 10	- 10	- 19	+ 19
After	7 u	1 u	4 u	4 u

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

Total amount that Tommy and Diana have in the end for both cases
= 7 u + 1 u
= 8 u

Amount that Tommy and Diana each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Tommy has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 19
7 u - 4 u = 19 + 10

1 u = 29

Amount that Tommy has
= 4 u + 19
= 4 x 29 + 19
= 116 + 19
= $135

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

Answer(s): (a) $135; (b) $39