Jane had 280 pencils. ²₇ were blue and the rest were brown and green. The ratio of the number of brown pencils to the number of green pencils was 1 : 3. Jane 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 brown pencils than blue pencils did he have at first?
2. How many more blue pencils did he have to buy?

Blue pencils	Brown pencils	Green pencils	Total
2x4	5x4
	1x5	3x5
8 u	5 u	15 u	280

	Blue pencils	Brown pencils	Green pencils
Before	8 u	5 u	15 u
Change	+ ?
After	20 u	20 u
Comparing blue, brown and green pencils in the end	1	1

(a)
The total number of brown pencils and green pencils is repeated. Make the total number of brown pencils and green pencils the same.  LCM of 5 and 4 is 20.

Total number of pencils at first
= 8 u + 5 u + 15 u
= 28 u

28 u = 280

1 u = 280 ÷ 28 = 10

Number of less brown pencils than blue pencils at first
= 8 u - 5 u
= 3 u
= 3 x 10
= 30

(b)
Number of more blue pencils that Jane had to buy
= 20 u - 8 u
= 12 u
= 12 x 10
= 120

Answer(s): (a) 30; (b) 120