Luis had ¹₂ as many stamps as Archie. Archie had ²₃ as many stamps as Hazel. After Luis and Hazel gave 16 stamps to Archie, Archie had four times as many stamps as Luis. Hazel then had the same number of stamps as Archie.

1. What was the ratio of the number of stamps Luis had to the number of stamps Hazel had in the beginning? Answer in simplest form.
2. How many stamps did Archie have in the end?

Luis	Archie	Hazel
1	2
	2	3
1	2	3

(a)
The number of stamps that Archie is repeated.  

Ratio of the number of stamps that Luis had to the number of stamps that Hazel had in the beginning = 1 : 3

	Luis	Archie	Hazel	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 stamps at first and in the end remains unchanged. Make the total number of stamps the same. LCM of 6 and 9 is 18.

Number of stamps that Archie received from Luis and Hazel
= 2 x 16
= 32

Number of stamps that Archie received from Luis and Hazel
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

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