Ken had ¹₂ as many marbles as Ahmad. Ahmad had ²₃ as many marbles as Julie. After Ken and Julie gave 16 marbles to Ahmad, Ahmad had four times as many marbles as Ken. Julie then had the same number of marbles as Ahmad.

1. What was the ratio of the number of marbles Ken had to the number of marbles Julie had in the beginning? Answer in simplest form.
2. How many marbles did Ahmad have in the end?

Ken	Ahmad	Julie
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Ken had to the number of marbles that Julie had in the beginning = 1 : 3

	Ken	Ahmad	Julie	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 Ahmad received from Ken and Julie
= 2 x 16
= 32

Number of marbles that Ahmad received from Ken and Julie
= 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