Pierre had ³₄ as many coins as Flynn. Flynn had ⁴₇ as many coins as Barbara. After Pierre and Barbara gave 16 coins to Flynn, Flynn had thrice as many coins as Pierre. Barbara then had the same number of coins as Flynn.

1. What was the ratio of the number of coins Barbara had to the number of coins Pierre had in the beginning? Answer in simplest form.
2. How many coins did Flynn have in the end?

Pierre	Flynn	Barbara
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Barbara had to the number of coins that Pierre had in the beginning = 7 : 3

	Pierre	Flynn	Barbara	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 16	+ 32	- 16
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 Flynn received from Pierre and Barbara
= 2 x 16
= 32

Number of coins that Flynn received from Pierre and Barbara
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of coins that Ashley had in the end
= 6 u
= 6 x 8
= 48