Michael had ¹₂ as many erasers as David. David had ²₃ as many erasers as Mary. After Michael and Mary gave 24 erasers to David, David had four times as many erasers as Michael. Mary then had the same number of erasers as David.

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

Michael	David	Mary
1	2
	2	3
1	2	3

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

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

	Michael	David	Mary	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 24	+ 48	- 24
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 David received from Michael and Mary
= 2 x 24
= 48

Number of erasers that David received from Michael and Mary
= 2 x 1 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

Number of erasers that Ashley had in the end
= 8 u
= 8 x 12
= 96