Tommy had ¹₂ as many stamps as Howard. Howard had ²₃ as many stamps as Esther. After Tommy and Esther gave 4 stamps to Howard, Howard had four times as many stamps as Tommy. Esther then had the same number of stamps as Howard.

1. What was the ratio of the number of stamps Tommy had to the number of stamps Esther had in the beginning? Answer in simplest form.
2. How many stamps did Howard have in the end?

Tommy	Howard	Esther
1	2
	2	3
1	2	3

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

Ratio of the number of stamps that Tommy had to the number of stamps that Esther had in the beginning = 1 : 3

	Tommy	Howard	Esther	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 4	+ 8	- 4
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 Howard received from Tommy and Esther
= 2 x 4
= 8

Number of stamps that Howard received from Tommy and Esther
= 2 x 1 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Number of stamps that Ashley had in the end
= 8 u
= 8 x 2
= 16