Valen had ¹₂ as many erasers as Sam. Sam had ²₃ as many erasers as Joelle. After Valen and Joelle gave 24 erasers to Sam, Sam had four times as many erasers as Valen. Joelle then had the same number of erasers as Sam.

1. What was the ratio of the number of erasers Valen had to the number of erasers Joelle had in the beginning? Answer in simplest form.
2. How many erasers did Sam have in the end?

Valen	Sam	Joelle
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Valen had to the number of erasers that Joelle had in the beginning = 1 : 3

	Valen	Sam	Joelle	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 Sam received from Valen and Joelle
= 2 x 24
= 48

Number of erasers that Sam received from Valen and Joelle
= 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