Julian had ³₄ as many stickers as Cole. Cole had ⁴₇ as many stickers as Ivory. After Julian and Ivory gave 20 stickers to Cole, Cole had thrice as many stickers as Julian. Ivory then had the same number of stickers as Cole.

1. What was the ratio of the number of stickers Ivory had to the number of stickers Julian had in the beginning? Answer in simplest form.
2. How many stickers did Cole have in the end?

Julian	Cole	Ivory
3	4
	4	7
3	4	7

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

Ratio of the number of stickers that Ivory had to the number of stickers that Julian had in the beginning = 7 : 3

	Julian	Cole	Ivory	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 Cole received from Julian and Ivory
= 2 x 20
= 40

Number of stickers that Cole received from Julian and Ivory
= 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