Diana had 42 pencils. ³₇ were gold and the rest were blue and white. The ratio of the number of blue pencils to the number of white pencils was 1 : 2. Diana decided to buy some more gold pencils to increase the number of gold pencils to half of the total number of pencils.

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

Gold pencils	Blue pencils	White pencils	Total
3x3	4x3
	1x4	2x4
9 u	4 u	8 u	42

	Gold pencils	Blue pencils	White pencils
Before	9 u	4 u	8 u
Change	+ ?
After	12 u	12 u
Comparing gold, blue and white pencils in the end	1	1

(a)
The total number of blue pencils and white pencils is repeated. Make the total number of blue pencils and white 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 = 42

1 u = 42 ÷ 21 = 2

Number of less blue pencils than gold pencils at first
= 9 u - 4 u
= 5 u
= 5 x 2
= 10

(b)
Number of more gold pencils that Diana had to buy
= 12 u - 9 u
= 3 u
= 3 x 2
= 6

Answer(s): (a) 10; (b) 6