Asher had ¹₂ as many erasers as Ivan. Ivan had ²₃ as many erasers as Yen. After Asher and Yen gave 8 erasers to Ivan, Ivan had four times as many erasers as Asher. Yen then had the same number of erasers as Ivan.

1. What was the ratio of the number of erasers Asher had to the number of erasers Yen had in the beginning? Answer in simplest form.
2. How many erasers did Ivan have in the end?

Asher	Ivan	Yen
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Asher had to the number of erasers that Yen had in the beginning = 1 : 3

	Asher	Ivan	Yen	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 8	+ 16	- 8
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 Ivan received from Asher and Yen
= 2 x 8
= 16

Number of erasers that Ivan received from Asher and Yen
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of erasers that Ashley had in the end
= 8 u
= 8 x 4
= 32