Xavier had ³₄ as many coins as Ryan. Ryan had ⁴₇ as many coins as Sarah. After Xavier and Sarah gave 12 coins to Ryan, Ryan had thrice as many coins as Xavier. Sarah then had the same number of coins as Ryan.

1. What was the ratio of the number of coins Sarah had to the number of coins Xavier had in the beginning? Answer in simplest form.
2. How many coins did Ryan have in the end?

Xavier	Ryan	Sarah
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Sarah had to the number of coins that Xavier had in the beginning = 7 : 3

	Xavier	Ryan	Sarah	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of coins at first and in the end remains unchanged. Make the total number of coins the same. LCM of 14 and 7 is 14.

Number of coins that Ryan received from Xavier and Sarah
= 2 x 12
= 24

Number of coins that Ryan received from Xavier and Sarah
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of coins that Ashley had in the end
= 6 u
= 6 x 6
= 36