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

1. Find the ratio of the number of white pencils to the number of purple pencils.
2. There were 154 fewer silver pencils than purple pencils. How many pencils were there in the bag?

Purple pencils	Silver pencils	White pencils
3x5	2x5
	4x2	1x2
15 u	8 u	2 u

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

Remaining fraction of silver pencils = ⁴₅
Remaining fraction of white pencils = 1 - ⁴₅ = ¹₅

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

White pencils : Purple pencils
2 : 15

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

7 u = 154
1 u = 154 ÷ 7 = 22

Total number of pencils
= 15 u + 8 u + 2 u
= 25 u
= 25 x 22
= 550

Answer(s): (a) 2 : 15; (b) 550