Zeph had ³₄ as many stickers as Warren. Warren had ⁴₇ as many stickers as Kathy. After Zeph and Kathy gave 20 stickers to Warren, Warren had thrice as many stickers as Zeph. Kathy then had the same number of stickers as Warren.

1. What was the ratio of the number of stickers Zeph had to the number of stickers Kathy had in the beginning? Answer in simplest form.
2. How many stickers did Warren have in the end?

Zeph	Warren	Kathy
3	4
	4	7
3	4	7

(a)
The number of stickers that Warren is repeated.  

Ratio of the number of stickers that Zeph had to the number of stickers that Kathy had in the beginning = 3 : 7

	Zeph	Warren	Kathy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 20	+ 40	- 20
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of stickers at first and in the end remains unchanged. Make the total number of stickers the same. LCM of 14 and 7 is 14.

Number of stickers that Warren received from Zeph and Kathy
= 2 x 20
= 40

Number of stickers that Warren received from Zeph and Kathy
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of stickers that Ashley had in the end
= 6 u
= 6 x 10
= 60