Fabian and Dana has some money each. If Dana gives Fabian $13, he will have 7 times as much money as her. If Fabian gives Dana $10, he will have the same amount of money as her. How much money does each person have respectively?

1. Fabian?
2. Dana?

	Case 1		Case 2
	Fabian	Dana	Fabian	Dana
Before	7 u - 13	1 u + 13	4 u + 10	4 u - 10
Change	+ 13	- 13	- 10	+ 10
After	7 u	1 u	4 u	4 u

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

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

Amount that Fabian and Dana each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Fabian has at first in Case 1 and Case 2 is the same.
7 u - 13 = 4 u + 10
7 u - 4 u = 10 + 13

1 u = 23

Amount that Fabian has
= 4 u + 10
= 4 x 23 + 10
= 92 + 10
= $102

(b)
Amount that Dana has
= 1 u + 13
= 23 + 13
= $36

Answer(s): (a) $102; (b) $36