Tom had ³₄ as many marbles as Riordan. Riordan had ⁴₇ as many marbles as Gabby. After Tom and Gabby gave 26 marbles to Riordan, Riordan had thrice as many marbles as Tom. Gabby then had the same number of marbles as Riordan.

1. What was the ratio of the number of marbles Tom had to the number of marbles Gabby had in the beginning? Answer in simplest form.
2. How many marbles did Riordan have in the end?

Tom	Riordan	Gabby
3	4
	4	7
3	4	7

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

Ratio of the number of marbles that Tom had to the number of marbles that Gabby had in the beginning = 3 : 7

	Tom	Riordan	Gabby	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 26	+ 52	- 26
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 Riordan received from Tom and Gabby
= 2 x 26
= 52

Number of marbles that Riordan received from Tom and Gabby
= 2 x 1 u
= 2 u

2 u = 26

1 u = 26 ÷ 2 = 13

Number of marbles that Ashley had in the end
= 6 u
= 6 x 13
= 78