David and Nicole has some money each. If Nicole gives David $13, he will have 7 times as much money as her. If David gives Nicole $19, he will have the same amount of money as her. How much money does each person have respectively?

1. David?
2. Nicole?

	Case 1		Case 2
	David	Nicole	David	Nicole
Before	7 u - 13	1 u + 13	4 u + 19	4 u - 19
Change	+ 13	- 13	- 19	+ 19
After	7 u	1 u	4 u	4 u

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

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

Amount that David and Nicole each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that David has at first in Case 1 and Case 2 is the same.
7 u - 13 = 4 u + 19
7 u - 4 u = 19 + 13

1 u = 32

Amount that David has
= 4 u + 19
= 4 x 32 + 19
= 128 + 19
= $147

(b)
Amount that Nicole has
= 1 u + 13
= 32 + 13
= $45

Answer(s): (a) $147; (b) $45