A packet contained black, purple and grey pencils. ²₅ of the pencils were black and ⁴₉ of the remainder were purple pencils.The rest were grey pencils.

1. Find the ratio of the number of grey pencils to the number of black pencils.
2. There were 200 fewer purple pencils than black pencils. How many pencils were there in the packet?

Black pencils	Purple pencils	Grey pencils
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

(a)
Fraction of black pencils = ²₅
Fraction of pencils that are not black = 1 - ²₅ = ³₅

Remaining fraction of purple pencils = ⁴₉
Remaining fraction of grey pencils = 1 - ⁴₉ = ⁵₉

The total number of purple pencils and grey pencils is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 9 = 9

Grey pencils : Black pencils
5 : 6

(b)
Difference in the number of black pencils and purple pencils
= 6 u - 4 u
= 2 u

2 u = 200
1 u = 200 ÷ 2 = 100

Total number of pencils
= 6 u + 4 u + 5 u
= 15 u
= 15 x 100
= 1500

Answer(s): (a) 5 : 6; (b) 1500