Billy had ³₄ as many erasers as Albert. Albert had ⁴₇ as many erasers as Rachel. After Billy and Rachel gave 16 erasers to Albert, Albert had thrice as many erasers as Billy. Rachel then had the same number of erasers as Albert.

1. What was the ratio of the number of erasers Billy had to the number of erasers Rachel had in the beginning? Answer in simplest form.
2. How many erasers did Albert have in the end?

Billy	Albert	Rachel
3	4
	4	7
3	4	7

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

Ratio of the number of erasers that Billy had to the number of erasers that Rachel had in the beginning = 3 : 7

	Billy	Albert	Rachel	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 16	+ 32	- 16
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 Albert received from Billy and Rachel
= 2 x 16
= 32

Number of erasers that Albert received from Billy and Rachel
= 2 x 1 u
= 2 u

2 u = 16

1 u = 16 ÷ 2 = 8

Number of erasers that Ashley had in the end
= 6 u
= 6 x 8
= 48