Caden had ³₄ as many erasers as John. John had ⁴₇ as many erasers as Tammy. After Caden and Tammy gave 24 erasers to John, John had thrice as many erasers as Caden. Tammy then had the same number of erasers as John.

1. What was the ratio of the number of erasers Tammy had to the number of erasers Caden had in the beginning? Answer in simplest form.
2. How many erasers did John have in the end?

Caden	John	Tammy
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Tammy had to the number of erasers that Caden had in the beginning = 7 : 3

	Caden	John	Tammy	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 24	+ 48	- 24
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 John received from Caden and Tammy
= 2 x 24
= 48

Number of erasers that John received from Caden and Tammy
= 2 x 1 u
= 2 u

2 u = 24

1 u = 24 ÷ 2 = 12

Number of erasers that Ashley had in the end
= 6 u
= 6 x 12
= 72