Dylan and Jane has some money each. If Jane gives Dylan $13, he will have 5 times as much money as her. If Dylan gives Jane $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Dylan?
2. Jane?

	Case 1		Case 2
	Dylan	Jane	Dylan	Jane
Before	5 u - 13	1 u + 13	3 u + 19	3 u - 19
Change	+ 13	- 13	- 19	+ 19
After	5 u	1 u	3 u	3 u

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

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

Amount that Dylan and Jane each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Dylan has at first in Case 1 and Case 2 is the same.
5 u - 13 = 3 u + 19
5 u - 3 u = 19 + 13

1 u = 32

Amount that Dylan has
= 3 u + 19
= 3 x 32 + 19
= 96 + 19
= $115

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

Answer(s): (a) $115; (b) $45