Cole had ¹₂ as many cards as Zeph. Zeph had ²₃ as many cards as Cindy. After Cole and Cindy gave 20 cards to Zeph, Zeph had four times as many cards as Cole. Cindy then had the same number of cards as Zeph.

1. What was the ratio of the number of cards Cindy had to the number of cards Cole had in the beginning? Answer in simplest form.
2. How many cards did Zeph have in the end?

Cole	Zeph	Cindy
1	2
	2	3
1	2	3

(a)
The number of cards that Zeph is repeated.  

Ratio of the number of cards that Cindy had to the number of cards that Cole had in the beginning = 3 : 1

	Cole	Zeph	Cindy	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 20	+ 40	- 20
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of cards at first and in the end remains unchanged. Make the total number of cards the same. LCM of 6 and 9 is 18.

Number of cards that Zeph received from Cole and Cindy
= 2 x 20
= 40

Number of cards that Zeph received from Cole and Cindy
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of cards that Ashley had in the end
= 8 u
= 8 x 10
= 80