Ian had ³₄ as many stickers as Charlie. Charlie had ⁴₇ as many stickers as Diana. After Ian and Diana gave 20 stickers to Charlie, Charlie had thrice as many stickers as Ian. Diana then had the same number of stickers as Charlie.

1. What was the ratio of the number of stickers Diana had to the number of stickers Ian had in the beginning? Answer in simplest form.
2. How many stickers did Charlie have in the end?

Ian	Charlie	Diana
3	4
	4	7
3	4	7

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

Ratio of the number of stickers that Diana had to the number of stickers that Ian had in the beginning = 7 : 3

	Ian	Charlie	Diana	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 Charlie received from Ian and Diana
= 2 x 20
= 40

Number of stickers that Charlie received from Ian and Diana
= 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