Michael had ¹₂ as many erasers as Tom. Tom had ²₃ as many erasers as Zara. After Michael and Zara gave 28 erasers to Tom, Tom had four times as many erasers as Michael. Zara then had the same number of erasers as Tom.

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

Michael	Tom	Zara
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Zara had to the number of erasers that Michael had in the beginning = 3 : 1

	Michael	Tom	Zara	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 28	+ 56	- 28
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of erasers at first and in the end remains unchanged. Make the total number of erasers the same. LCM of 6 and 9 is 18.

Number of erasers that Tom received from Michael and Zara
= 2 x 28
= 56

Number of erasers that Tom received from Michael and Zara
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of erasers that Ashley had in the end
= 8 u
= 8 x 14
= 112