Hazel had 168 pencils. ³₇ were brown and the rest were blue and gold. The ratio of the number of blue pencils to the number of gold pencils was 1 : 5. Hazel decided to buy some more brown pencils to increase the number of brown pencils to half of the total number of pencils.

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

Brown pencils	Blue pencils	Gold pencils	Total
3x3	4x3
	1x2	5x2
9 u	2 u	10 u	168

	Brown pencils	Blue pencils	Gold pencils
Before	9 u	2 u	10 u
Change	+ ?
After	12 u	12 u
Comparing brown, blue and gold pencils in the end	1	1

(a)
The total number of blue pencils and gold pencils is repeated. Make the total number of blue pencils and gold pencils the same.  LCM of 4 and 6 is 12.

Total number of pencils at first
= 9 u + 2 u + 10 u
= 21 u

21 u = 168

1 u = 168 ÷ 21 = 8

Number of less blue pencils than brown pencils at first
= 9 u - 2 u
= 7 u
= 7 x 8
= 56

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

Answer(s): (a) 56; (b) 24