Bobby had ¹₂ as many marbles as Jenson. Jenson had ²₃ as many marbles as Shiyun. After Bobby and Shiyun gave 16 marbles to Jenson, Jenson had four times as many marbles as Bobby. Shiyun then had the same number of marbles as Jenson.

1. What was the ratio of the number of marbles Shiyun had to the number of marbles Bobby had in the beginning? Answer in simplest form.
2. How many marbles did Jenson have in the end?

Bobby	Jenson	Shiyun
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Shiyun had to the number of marbles that Bobby had in the beginning = 3 : 1

	Bobby	Jenson	Shiyun	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 16	+ 32	- 16
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of marbles at first and in the end remains unchanged. Make the total number of marbles the same. LCM of 6 and 9 is 18.

Number of marbles that Jenson received from Bobby and Shiyun
= 2 x 16
= 32

Number of marbles that Jenson received from Bobby and Shiyun
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of marbles that Ashley had in the end
= 8 u
= 8 x 8
= 64