Cody had ¹₂ as many buttons as Glen. Glen had ²₃ as many buttons as Betty. After Cody and Betty gave 4 buttons to Glen, Glen had four times as many buttons as Cody. Betty then had the same number of buttons as Glen.

1. What was the ratio of the number of buttons Cody had to the number of buttons Betty had in the beginning? Answer in simplest form.
2. How many buttons did Glen have in the end?

Cody	Glen	Betty
1	2
	2	3
1	2	3

(a)
The number of buttons that Glen is repeated.  

Ratio of the number of buttons that Cody had to the number of buttons that Betty had in the beginning = 1 : 3

	Cody	Glen	Betty	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 buttons at first and in the end remains unchanged. Make the total number of buttons the same. LCM of 6 and 9 is 18.

Number of buttons that Glen received from Cody and Betty
= 2 x 4
= 8

Number of buttons that Glen received from Cody and Betty
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

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