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

1. Find the ratio of the number of yellow pencils to the number of green pencils.
2. There were 140 fewer purple pencils than green pencils. How many pencils were there in the bag?

Green pencils	Purple pencils	Yellow 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 yellow pencils = 1 - ⁴₉ = ⁵₉

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

Yellow pencils : Green pencils
5 : 6

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

2 u = 140
1 u = 140 ÷ 2 = 70

Total number of pencils
= 6 u + 4 u + 5 u
= 15 u
= 15 x 70
= 1050

Answer(s): (a) 5 : 6; (b) 1050