Archie had ³₄ as many erasers as Tom. Tom had ⁴₇ as many erasers as Kathy. After Archie and Kathy gave 6 erasers to Tom, Tom had thrice as many erasers as Archie. Kathy then had the same number of erasers as Tom.

1. What was the ratio of the number of erasers Kathy had to the number of erasers Archie had in the beginning? Answer in simplest form.
2. How many erasers did Tom have in the end?

Archie	Tom	Kathy
3	4
	4	7
3	4	7

(a)
The number of erasers that Tom is repeated.  

Ratio of the number of erasers that Kathy had to the number of erasers that Archie had in the beginning = 7 : 3

	Archie	Tom	Kathy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 6	+ 12	- 6
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

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

Number of erasers that Tom received from Archie and Kathy
= 2 x 6
= 12

Number of erasers that Tom received from Archie and Kathy
= 2 x 1 u
= 2 u

2 u = 6

1 u = 6 ÷ 2 = 3

Number of erasers that Ashley had in the end
= 6 u
= 6 x 3
= 18