Reggie had ¹₂ as many erasers as Tim. Tim had ²₃ as many erasers as Mary. After Reggie and Mary gave 30 erasers to Tim, Tim had four times as many erasers as Reggie. Mary then had the same number of erasers as Tim.

1. What was the ratio of the number of erasers Reggie had to the number of erasers Mary had in the beginning? Answer in simplest form.
2. How many erasers did Tim have in the end?

Reggie	Tim	Mary
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Reggie had to the number of erasers that Mary had in the beginning = 1 : 3

	Reggie	Tim	Mary	Total
Before	1x3 = 3 u	2x3 = 6 u	3x3 = 9 u	6x3 = 18 u
Change	- 30	+ 60	- 30
After	1x2 = 2 u	4x2 = 8 u	4x2 = 8 u	9x2 = 18 u

The total number of erasers at first and in the end remains unchanged. Make the total number of erasers the same. LCM of 6 and 9 is 18.

Number of erasers that Tim received from Reggie and Mary
= 2 x 30
= 60

Number of erasers that Tim received from Reggie and Mary
= 2 x 1 u
= 2 u

2 u = 30

1 u = 30 ÷ 2 = 15

Number of erasers that Ashley had in the end
= 8 u
= 8 x 15
= 120