Will and Natalie has some money each. If Natalie gives Will $16, he will have 7 times as much money as her. If Will gives Natalie $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Will?
2. Natalie?

	Case 1		Case 2
	Will	Natalie	Will	Natalie
Before	7 u - 16	1 u + 16	4 u + 19	4 u - 19
Change	+ 16	- 16	- 19	+ 19
After	7 u	1 u	4 u	4 u

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

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

Amount that Will and Natalie each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Will has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 19
7 u - 4 u = 19 + 16

1 u = 35

Amount that Will has
= 4 u + 19
= 4 x 35 + 19
= 140 + 19
= $159

(b)
Amount that Natalie has
= 1 u + 16
= 35 + 16
= $51

Answer(s): (a) $159; (b) $51