Nicole had 80 pencils. ²₅ were green and the rest were grey and black. The ratio of the number of grey pencils to the number of black pencils was 1 : 3. Nicole decided to buy some more green pencils to increase the number of green pencils to half of the total number of pencils.

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

Green pencils	Grey pencils	Black pencils	Total
2x4	3x4
	1x3	3x3
8 u	3 u	9 u	80

	Green pencils	Grey pencils	Black pencils
Before	8 u	3 u	9 u
Change	+ ?
After	12 u	12 u
Comparing green, grey and black pencils in the end	1	1

(a)
The total number of grey pencils and black pencils is repeated. Make the total number of grey pencils and black pencils the same.  LCM of 3 and 4 is 12.

Total number of pencils at first
= 8 u + 3 u + 9 u
= 20 u

20 u = 80

1 u = 80 ÷ 20 = 4

Number of less grey pencils than green pencils at first
= 8 u - 3 u
= 5 u
= 5 x 4
= 20

(b)
Number of more green pencils that Nicole had to buy
= 12 u - 8 u
= 4 u
= 4 x 4
= 16

Answer(s): (a) 20; (b) 16