Ben had ¹₂ as many coins as Asher. Asher had ²₃ as many coins as Gabby. After Ben and Gabby gave 18 coins to Asher, Asher had four times as many coins as Ben. Gabby then had the same number of coins as Asher.

1. What was the ratio of the number of coins Ben had to the number of coins Gabby had in the beginning? Answer in simplest form.
2. How many coins did Asher have in the end?

Ben	Asher	Gabby
1	2
	2	3
1	2	3

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

Ratio of the number of coins that Ben had to the number of coins that Gabby had in the beginning = 1 : 3

	Ben	Asher	Gabby	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 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 Asher received from Ben and Gabby
= 2 x 18
= 36

Number of coins that Asher received from Ben and Gabby
= 2 x 1 u
= 2 u

2 u = 18

1 u = 18 ÷ 2 = 9

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