Glen had ¹₂ as many coins as Andy. Andy had ²₃ as many coins as Gem. After Glen and Gem gave 22 coins to Andy, Andy had four times as many coins as Glen. Gem then had the same number of coins as Andy.

1. What was the ratio of the number of coins Glen had to the number of coins Gem had in the beginning? Answer in simplest form.
2. How many coins did Andy have in the end?

Glen	Andy	Gem
1	2
	2	3
1	2	3

(a)
The number of coins that Andy is repeated.  

Ratio of the number of coins that Glen had to the number of coins that Gem had in the beginning = 1 : 3

	Glen	Andy	Gem	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 22	+ 44	- 22
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

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

Number of coins that Andy received from Glen and Gem
= 2 x 22
= 44

Number of coins that Andy received from Glen and Gem
= 2 x 1 u
= 2 u

2 u = 22

1 u = 22 ÷ 2 = 11

Number of coins that Ashley had in the end
= 8 u
= 8 x 11
= 88