Julian had 45 erasers. ⁴₅ were grey and the rest were silver and pink. The ratio of the number of silver erasers to the number of pink erasers was 1 : 2. Julian decided to give away some grey erasers to decrease the number of grey erasers to half of the total number of erasers.

1. How many more grey erasers than silver erasers did he have at first?
2. How many grey erasers did he have to give away?

Grey erasers	Silver erasers	Pink erasers	Total
4x3	1x3
	1x1	2x1
12 u	1 u	2 u	45

	Grey erasers	Silver erasers	Pink erasers
Before	12 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing grey, silver and pink erasers in the end	1	1

(a)
The total number of silver erasers and pink erasers is repeated. Make the total number of silver erasers and pink erasers the same.  LCM of 1 and 3 is 3.

Total number of erasers at first
= 12 u + 1 u + 2 u
= 15 u

15 u = 45

1 u = 45 ÷ 15 = 3

Number of more grey erasers than silver erasers at first
= 12 u - 1 u
= 11 u
= 11 x 3
= 33

(b)
Number of more grey erasers that Julian had to give away
= 12 u - 3 u
= 9 u
= 9 x 3
= 27

Answer(s): (a) 33; (b) 27