Daniel had ¹₂ as many stickers as John. John had ²₃ as many stickers as Cathy. After Daniel and Cathy gave 4 stickers to John, John had four times as many stickers as Daniel. Cathy then had the same number of stickers as John.

1. What was the ratio of the number of stickers Daniel had to the number of stickers Cathy had in the beginning? Answer in simplest form.
2. How many stickers did John have in the end?

Daniel	John	Cathy
1	2
	2	3
1	2	3

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

Ratio of the number of stickers that Daniel had to the number of stickers that Cathy had in the beginning = 1 : 3

	Daniel	John	Cathy	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 4	+ 8	- 4
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of stickers that John received from Daniel and Cathy
= 2 x 4
= 8

Number of stickers that John received from Daniel and Cathy
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of stickers that Ashley had in the end
= 8 u
= 8 x 2
= 16