Oliver had ³₄ as many erasers as Charlie. Charlie had ⁴₇ as many erasers as Zara. After Oliver and Zara gave 30 erasers to Charlie, Charlie had thrice as many erasers as Oliver. Zara then had the same number of erasers as Charlie.

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

Oliver	Charlie	Zara
3	4
	4	7
3	4	7

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

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

	Oliver	Charlie	Zara	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 30	+ 60	- 30
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 Charlie received from Oliver and Zara
= 2 x 30
= 60

Number of erasers that Charlie received from Oliver and Zara
= 2 x 1 u
= 2 u

2 u = 30

1 u = 30 ÷ 2 = 15

Number of erasers that Ashley had in the end
= 6 u
= 6 x 15
= 90