Liam had 45 pencils. ⁴₅ were white and the rest were silver and blue. The ratio of the number of silver pencils to the number of blue pencils was 1 : 2. Liam decided to give away some white pencils to decrease the number of white pencils to half of the total number of pencils.

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

White pencils	Silver pencils	Blue pencils	Total
4x3	1x3
	1x1	2x1
12 u	1 u	2 u	45

	White pencils	Silver pencils	Blue pencils
Before	12 u	1 u	2 u
Change	- ?
After	3 u	3 u
Comparing white, silver and blue pencils in the end	1	1

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

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

15 u = 45

1 u = 45 ÷ 15 = 3

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

(b)
Number of more white pencils that Liam had to give away
= 12 u - 3 u
= 9 u
= 9 x 3
= 27

Answer(s): (a) 33; (b) 27