Howard had ¹₂ as many marbles as Andy. Andy had ²₃ as many marbles as Tiffany. After Howard and Tiffany gave 16 marbles to Andy, Andy had four times as many marbles as Howard. Tiffany then had the same number of marbles as Andy.

1. What was the ratio of the number of marbles Howard had to the number of marbles Tiffany had in the beginning? Answer in simplest form.
2. How many marbles did Andy have in the end?

Howard	Andy	Tiffany
1	2
	2	3
1	2	3

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

Ratio of the number of marbles that Howard had to the number of marbles that Tiffany had in the beginning = 1 : 3

	Howard	Andy	Tiffany	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 Andy received from Howard and Tiffany
= 2 x 16
= 32

Number of marbles that Andy received from Howard and Tiffany
= 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