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

1. Zane?
2. Lucy?

	Case 1		Case 2
	Zane	Lucy	Zane	Lucy
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 Lucy gives Zane some money or Zane gives Lucy some money, the total amount of money remains the same.  

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

Amount that Zane and Lucy each has in the end in Case 2
= 6 u ÷ 2
= 3 u

The amount that Zane 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 Zane has
= 3 u + 10
= 3 x 23 + 10
= 69 + 10
= $79

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

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