Rael had ³₄ as many erasers as Sam. Sam had ⁴₇ as many erasers as Jaslyn. After Rael and Jaslyn gave 20 erasers to Sam, Sam had thrice as many erasers as Rael. Jaslyn then had the same number of erasers as Sam.

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

Rael	Sam	Jaslyn
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Jaslyn had to the number of erasers that Rael had in the beginning = 7 : 3

	Rael	Sam	Jaslyn	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 20	+ 40	- 20
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of erasers at first and in the end remains unchanged. Make the total number of erasers the same. LCM of 14 and 7 is 14.

Number of erasers that Sam received from Rael and Jaslyn
= 2 x 20
= 40

Number of erasers that Sam received from Rael and Jaslyn
= 2 x 1 u
= 2 u

2 u = 20

1 u = 20 ÷ 2 = 10

Number of erasers that Ashley had in the end
= 6 u
= 6 x 10
= 60