Paul had 112 pencils. ⁴₇ were purple and the rest were grey and green. The ratio of the number of grey pencils to the number of green pencils was 1 : 5. Paul decided to give away some purple pencils to decrease the number of purple pencils to half of the total number of pencils.

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

Purple pencils	Grey pencils	Green pencils	Total
4x2	3x2
	1x1	5x1
8 u	1 u	5 u	112

	Purple pencils	Grey pencils	Green pencils
Before	8 u	1 u	5 u
Change	- ?
After	6 u	6 u
Comparing purple, grey and green pencils in the end	1	1

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

Total number of pencils at first
= 8 u + 1 u + 5 u
= 14 u

14 u = 112

1 u = 112 ÷ 14 = 8

Number of more purple pencils than grey pencils at first
= 8 u - 1 u
= 7 u
= 7 x 8
= 56

(b)
Number of more purple pencils that Paul had to give away
= 8 u - 6 u
= 2 u
= 2 x 8
= 16

Answer(s): (a) 56; (b) 16