A bag contained blue, purple and pink pencils. ⁴₅ of the pencils were blue and ⁴₅ of the remainder were purple pencils.The rest were pink pencils.

1. Find the ratio of the number of pink pencils to the number of blue pencils.
2. There were 144 fewer purple pencils than blue pencils. How many pencils were there in the bag?

Blue pencils	Purple pencils	Pink pencils
4x5	1x5
	4x1	1x1
20 u	4 u	1 u

(a)
Fraction of blue pencils = ⁴₅
Fraction of pencils that are not blue = 1 - ⁴₅ = ¹₅

Remaining fraction of purple pencils = ⁴₅
Remaining fraction of pink pencils = 1 - ⁴₅ = ¹₅

The total number of purple pencils and pink pencils is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 1 and 5 = 5

Pink pencils : Blue pencils
1 : 20

(b)
Difference in the number of blue pencils and purple pencils
= 20 u - 4 u
= 16 u

16 u = 144
1 u = 144 ÷ 16 = 9

Total number of pencils
= 20 u + 4 u + 1 u
= 25 u
= 25 x 9
= 225

Answer(s): (a) 1 : 20; (b) 225