Michael had ¹₂ as many coins as Dylan. Dylan had ²₃ as many coins as Tammy. After Michael and Tammy gave 22 coins to Dylan, Dylan had four times as many coins as Michael. Tammy then had the same number of coins as Dylan.

1. What was the ratio of the number of coins Tammy had to the number of coins Michael had in the beginning? Answer in simplest form.
2. How many coins did Dylan have in the end?

Michael	Dylan	Tammy
1	2
	2	3
1	2	3

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

Ratio of the number of coins that Tammy had to the number of coins that Michael had in the beginning = 3 : 1

	Michael	Dylan	Tammy	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 Dylan received from Michael and Tammy
= 2 x 22
= 44

Number of coins that Dylan received from Michael and Tammy
= 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