Xavier had ¹₂ as many erasers as Liam. Liam had ²₃ as many erasers as Erika. After Xavier and Erika gave 20 erasers to Liam, Liam had four times as many erasers as Xavier. Erika then had the same number of erasers as Liam.

1. What was the ratio of the number of erasers Erika had to the number of erasers Xavier had in the beginning? Answer in simplest form.
2. How many erasers did Liam have in the end?

Xavier	Liam	Erika
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Erika had to the number of erasers that Xavier had in the beginning = 3 : 1

	Xavier	Liam	Erika	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 20	+ 40	- 20
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 Liam received from Xavier and Erika
= 2 x 20
= 40

Number of erasers that Liam received from Xavier and Erika
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of erasers that Ashley had in the end
= 8 u
= 8 x 10
= 80