A bag contained pink, brown and green pencils. ³₅ of the pencils were pink and ⁷₉ of the remainder were brown pencils.The rest were green pencils.

1. Find the ratio of the number of green pencils to the number of pink pencils.
2. There were 195 fewer brown pencils than pink pencils. How many pencils were there in the bag?

Pink pencils	Brown pencils	Green pencils
3x9	2x9
	7x2	2x2
27 u	14 u	4 u

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

Remaining fraction of brown pencils = ⁷₉
Remaining fraction of green pencils = 1 - ⁷₉ = ²₉

The total number of brown pencils and green pencils is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 2 and 9 = 18

Green pencils : Pink pencils
4 : 27

(b)
Difference in the number of pink pencils and brown pencils
= 27 u - 14 u
= 13 u

13 u = 195
1 u = 195 ÷ 13 = 15

Total number of pencils
= 27 u + 14 u + 4 u
= 45 u
= 45 x 15
= 675

Answer(s): (a) 4 : 27; (b) 675