Irene had 168 pencils. ³₇ were blue and the rest were grey and brown. The ratio of the number of grey pencils to the number of brown pencils was 1 : 2. Irene decided to buy some more blue pencils to increase the number of blue pencils to half of the total number of pencils.

1. How many less grey pencils than blue pencils did he have at first?
2. How many more blue pencils did he have to buy?

Blue pencils	Grey pencils	Brown pencils	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	168

	Blue pencils	Grey pencils	Brown pencils
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing blue, grey and brown pencils in the end	1	1

(a)
The total number of grey pencils and brown pencils is repeated. Make the total number of grey pencils and brown pencils the same.  LCM of 4 and 3 is 12.

Total number of pencils at first
= 9 u + 4 u + 8 u
= 21 u

21 u = 168

1 u = 168 ÷ 21 = 8

Number of less grey pencils than blue pencils at first
= 9 u - 4 u
= 5 u
= 5 x 8
= 40

(b)
Number of more blue pencils that Irene had to buy
= 12 u - 9 u
= 3 u
= 3 x 8
= 24

Answer(s): (a) 40; (b) 24