Howard had ¹₂ as many erasers as Ahmad. Ahmad had ²₃ as many erasers as Erika. After Howard and Erika gave 30 erasers to Ahmad, Ahmad had four times as many erasers as Howard. Erika then had the same number of erasers as Ahmad.

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

Howard	Ahmad	Erika
1	2
	2	3
1	2	3

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

Ratio of the number of erasers that Howard had to the number of erasers that Erika had in the beginning = 1 : 3

	Howard	Ahmad	Erika	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 Ahmad received from Howard and Erika
= 2 x 30
= 60

Number of erasers that Ahmad received from Howard and Erika
= 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