Elijah had ³₄ as many marbles as Pierre. Pierre had ⁴₇ as many marbles as Irene. After Elijah and Irene gave 12 marbles to Pierre, Pierre had thrice as many marbles as Elijah. Irene then had the same number of marbles as Pierre.

1. What was the ratio of the number of marbles Elijah had to the number of marbles Irene had in the beginning? Answer in simplest form.
2. How many marbles did Pierre have in the end?

Elijah	Pierre	Irene
3	4
	4	7
3	4	7

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

Ratio of the number of marbles that Elijah had to the number of marbles that Irene had in the beginning = 3 : 7

	Elijah	Pierre	Irene	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 marbles at first and in the end remains unchanged. Make the total number of marbles the same. LCM of 14 and 7 is 14.

Number of marbles that Pierre received from Elijah and Irene
= 2 x 12
= 24

Number of marbles that Pierre received from Elijah and Irene
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

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