Oscar had 432 pencils. ⁵₆ were grey and the rest were purple and white. The ratio of the number of purple pencils to the number of white pencils was 1 : 5. Oscar decided to give away some grey pencils to decrease the number of grey pencils to half of the total number of pencils.

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

Grey pencils	Purple pencils	White pencils	Total
5x6	1x6
	1x1	5x1
30 u	1 u	5 u	432

	Grey pencils	Purple pencils	White pencils
Before	30 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing grey, purple and white pencils in the end	1	1

(a)
The total number of purple pencils and white pencils is repeated. Make the total number of purple pencils and white pencils the same.  LCM of 1 and 6 is 6.

Total number of pencils at first
= 30 u + 1 u + 5 u
= 36 u

36 u = 432

1 u = 432 ÷ 36 = 12

Number of more grey pencils than purple pencils at first
= 30 u - 1 u
= 29 u
= 29 x 12
= 348

(b)
Number of more grey pencils that Oscar had to give away
= 30 u - 6 u
= 24 u
= 24 x 12
= 288

Answer(s): (a) 348; (b) 288