John had 162 erasers. ⁵₆ were white and the rest were grey and red. The ratio of the number of grey erasers to the number of red erasers was 1 : 2. John decided to give away some white erasers to decrease the number of white erasers to half of the total number of erasers.

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

White erasers	Grey erasers	Red erasers	Total
5x3	1x3
	1x1	2x1
15 u	1 u	2 u	162

	White erasers	Grey erasers	Red erasers
Before	15 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing white, grey and red erasers in the end	1	1

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

Total number of erasers at first
= 15 u + 1 u + 2 u
= 18 u

18 u = 162

1 u = 162 ÷ 18 = 9

Number of more white erasers than grey erasers at first
= 15 u - 1 u
= 14 u
= 14 x 9
= 126

(b)
Number of more white erasers that John had to give away
= 15 u - 3 u
= 12 u
= 12 x 9
= 108

Answer(s): (a) 126; (b) 108