Tom had ³₄ as many erasers as Cole. Cole had ⁴₇ as many erasers as Tiffany. After Tom and Tiffany gave 28 erasers to Cole, Cole had thrice as many erasers as Tom. Tiffany then had the same number of erasers as Cole.

1. What was the ratio of the number of erasers Tom had to the number of erasers Tiffany had in the beginning? Answer in simplest form.
2. How many erasers did Cole have in the end?

Tom	Cole	Tiffany
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Tom had to the number of erasers that Tiffany had in the beginning = 3 : 7

	Tom	Cole	Tiffany	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 28	+ 56	- 28
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 Cole received from Tom and Tiffany
= 2 x 28
= 56

Number of erasers that Cole received from Tom and Tiffany
= 2 x 1 u
= 2 u

2 u = 28

1 u = 28 ÷ 2 = 14

Number of erasers that Ashley had in the end
= 6 u
= 6 x 14
= 84