Fabian and Usha has some money each. If Usha gives Fabian $13, he will have 5 times as much money as her. If Fabian gives Usha $10, he will have the same amount of money as her. How much money does each person have respectively?

1. Fabian?
2. Usha?

	Case 1		Case 2
	Fabian	Usha	Fabian	Usha
Before	5 u - 13	1 u + 13	3 u + 10	3 u - 10
Change	+ 13	- 13	- 10	+ 10
After	5 u	1 u	3 u	3 u

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

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

Amount that Fabian and Usha each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Fabian has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 10
5 u - 3 u = 10 + 13

1 u = 23

Amount that Fabian has
= 3 u + 10
= 3 x 23 + 10
= 69 + 10
= $79

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

Answer(s): (a) $79; (b) $36