A bag contained green, purple and blue pencils. ²₅ of the pencils were green and ⁴₉ of the remainder were purple pencils.The rest were blue pencils.

1. Find the ratio of the number of blue pencils to the number of green pencils.
2. There were 186 fewer purple pencils than green pencils. How many pencils were there in the bag?

Green pencils	Purple pencils	Blue pencils
2x3	3x3
	4x1	5x1
6 u	4 u	5 u

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

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

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

Blue pencils : Green pencils
5 : 6

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

2 u = 186
1 u = 186 ÷ 2 = 93

Total number of pencils
= 6 u + 4 u + 5 u
= 15 u
= 15 x 93
= 1395

Answer(s): (a) 5 : 6; (b) 1395