A bag contained red, yellow and purple pencils. ³₅ of the pencils were red and ⁴₅ of the remainder were yellow pencils.The rest were purple pencils.

1. Find the ratio of the number of purple pencils to the number of red pencils.
2. There were 147 fewer yellow pencils than red pencils. How many pencils were there in the bag?

Red pencils	Yellow pencils	Purple pencils
3x5	2x5
	4x2	1x2
15 u	8 u	2 u

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

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

The total number of yellow pencils and purple pencils is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 5 = 10

Purple pencils : Red pencils
2 : 15

(b)
Difference in the number of red pencils and yellow pencils
= 15 u - 8 u
= 7 u

7 u = 147
1 u = 147 ÷ 7 = 21

Total number of pencils
= 15 u + 8 u + 2 u
= 25 u
= 25 x 21
= 525

Answer(s): (a) 2 : 15; (b) 525