Elijah had ¹₂ as many coins as Reggie. Reggie had ²₃ as many coins as Tiffany. After Elijah and Tiffany gave 10 coins to Reggie, Reggie had four times as many coins as Elijah. Tiffany then had the same number of coins as Reggie.

1. What was the ratio of the number of coins Tiffany had to the number of coins Elijah had in the beginning? Answer in simplest form.
2. How many coins did Reggie have in the end?

Elijah	Reggie	Tiffany
1	2
	2	3
1	2	3

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

Ratio of the number of coins that Tiffany had to the number of coins that Elijah had in the beginning = 3 : 1

	Elijah	Reggie	Tiffany	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 10	+ 20	- 10
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 Reggie received from Elijah and Tiffany
= 2 x 10
= 20

Number of coins that Reggie received from Elijah and Tiffany
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of coins that Ashley had in the end
= 8 u
= 8 x 5
= 40