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

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

Howard	Zane	Tina
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Tina had to the number of erasers that Howard had in the beginning = 7 : 3

	Howard	Zane	Tina	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 Zane received from Howard and Tina
= 2 x 12
= 24

Number of erasers that Zane received from Howard and Tina
= 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