Ben had ³₄ as many coins as Ahmad. Ahmad had ⁴₇ as many coins as Winnie. After Ben and Winnie gave 12 coins to Ahmad, Ahmad had thrice as many coins as Ben. Winnie then had the same number of coins as Ahmad.

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

Ben	Ahmad	Winnie
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Winnie had to the number of coins that Ben had in the beginning = 7 : 3

	Ben	Ahmad	Winnie	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 Ahmad received from Ben and Winnie
= 2 x 12
= 24

Number of coins that Ahmad received from Ben and Winnie
= 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