Ian had ³₄ as many marbles as Eric. Eric had ⁴₇ as many marbles as Rachel. After Ian and Rachel gave 12 marbles to Eric, Eric had thrice as many marbles as Ian. Rachel then had the same number of marbles as Eric.

1. What was the ratio of the number of marbles Ian had to the number of marbles Rachel had in the beginning? Answer in simplest form.
2. How many marbles did Eric have in the end?

Ian	Eric	Rachel
3	4
	4	7
3	4	7

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

Ratio of the number of marbles that Ian had to the number of marbles that Rachel had in the beginning = 3 : 7

	Ian	Eric	Rachel	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 Eric received from Ian and Rachel
= 2 x 12
= 24

Number of marbles that Eric received from Ian and Rachel
= 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