Ahmad and Anna has some money each. If Anna gives Ahmad $13, he will have 5 times as much money as her. If Ahmad gives Anna $12, he will have the same amount of money as her. How much money does each person have respectively?

1. Ahmad?
2. Anna?

	Case 1		Case 2
	Ahmad	Anna	Ahmad	Anna
Before	5 u - 13	1 u + 13	3 u + 12	3 u - 12
Change	+ 13	- 13	- 12	+ 12
After	5 u	1 u	3 u	3 u

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

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

Amount that Ahmad and Anna each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Ahmad has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 12
5 u - 3 u = 12 + 13

1 u = 25

Amount that Ahmad has
= 3 u + 12
= 3 x 25 + 12
= 75 + 12
= $87

(b)
Amount that Anna has
= 1 u + 13
= 25 + 13
= $38

Answer(s): (a) $87; (b) $38