Jaslyn had 40 pencils. ²₅ were purple and the rest were brown and pink. The ratio of the number of brown pencils to the number of pink pencils was 1 : 5. Jaslyn decided to buy some more purple pencils to increase the number of purple pencils to half of the total number of pencils.

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

Purple pencils	Brown pencils	Pink pencils	Total
2x2	3x2
	1x1	5x1
4 u	1 u	5 u	40

	Purple pencils	Brown pencils	Pink pencils
Before	4 u	1 u	5 u
Change	+ ?
After	6 u	6 u
Comparing purple, brown and pink pencils in the end	1	1

(a)
The total number of brown pencils and pink pencils is repeated. Make the total number of brown pencils and pink pencils the same.  LCM of 3 and 6 is 6.

Total number of pencils at first
= 4 u + 1 u + 5 u
= 10 u

10 u = 40

1 u = 40 ÷ 10 = 4

Number of less brown pencils than purple pencils at first
= 4 u - 1 u
= 3 u
= 3 x 4
= 12

(b)
Number of more purple pencils that Jaslyn had to buy
= 6 u - 4 u
= 2 u
= 2 x 4
= 8

Answer(s): (a) 12; (b) 8