Jenson had ³₄ as many coins as Pierre. Pierre had ⁴₇ as many coins as Gem. After Jenson and Gem gave 10 coins to Pierre, Pierre had thrice as many coins as Jenson. Gem then had the same number of coins as Pierre.

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

Jenson	Pierre	Gem
3	4
	4	7
3	4	7

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

Ratio of the number of coins that Jenson had to the number of coins that Gem had in the beginning = 3 : 7

	Jenson	Pierre	Gem	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 10	+ 20	- 10
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 Pierre received from Jenson and Gem
= 2 x 10
= 20

Number of coins that Pierre received from Jenson and Gem
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of coins that Ashley had in the end
= 6 u
= 6 x 5
= 30