Charlie had ¹₂ as many buttons as Oliver. Oliver had ²₃ as many buttons as Xandra. After Charlie and Xandra gave 18 buttons to Oliver, Oliver had four times as many buttons as Charlie. Xandra then had the same number of buttons as Oliver.

1. What was the ratio of the number of buttons Charlie had to the number of buttons Xandra had in the beginning? Answer in simplest form.
2. How many buttons did Oliver have in the end?

Charlie	Oliver	Xandra
1	2
	2	3
1	2	3

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

Ratio of the number of buttons that Charlie had to the number of buttons that Xandra had in the beginning = 1 : 3

	Charlie	Oliver	Xandra	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 18	+ 36	- 18
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 Oliver received from Charlie and Xandra
= 2 x 18
= 36

Number of buttons that Oliver received from Charlie and Xandra
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

Number of buttons that Ashley had in the end
= 8 u
= 8 x 9
= 72