Archie had ³₄ as many stamps as Elijah. Elijah had ⁴₇ as many stamps as Abi. After Archie and Abi gave 28 stamps to Elijah, Elijah had thrice as many stamps as Archie. Abi then had the same number of stamps as Elijah.

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

Archie	Elijah	Abi
3	4
	4	7
3	4	7

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

Ratio of the number of stamps that Archie had to the number of stamps that Abi had in the beginning = 3 : 7

	Archie	Elijah	Abi	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of stamps at first and in the end remains unchanged. Make the total number of stamps the same. LCM of 14 and 7 is 14.

Number of stamps that Elijah received from Archie and Abi
= 2 x 28
= 56

Number of stamps that Elijah received from Archie and Abi
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of stamps that Ashley had in the end
= 6 u
= 6 x 14
= 84