Zane had ³₄ as many erasers as Simon. Simon had ⁴₇ as many erasers as Zara. After Zane and Zara gave 12 erasers to Simon, Simon had thrice as many erasers as Zane. Zara then had the same number of erasers as Simon.

1. What was the ratio of the number of erasers Zara had to the number of erasers Zane had in the beginning? Answer in simplest form.
2. How many erasers did Simon have in the end?

Zane	Simon	Zara
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Zara had to the number of erasers that Zane had in the beginning = 7 : 3

	Zane	Simon	Zara	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
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 Simon received from Zane and Zara
= 2 x 12
= 24

Number of erasers that Simon received from Zane and Zara
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of erasers that Ashley had in the end
= 6 u
= 6 x 6
= 36