A packet contained pink, red and white pencils. ²₅ of the pencils were pink and ³₈ of the remainder were red pencils.The rest were white pencils.

1. Find the ratio of the number of white pencils to the number of pink pencils.
2. There were 182 fewer red pencils than pink pencils. How many pencils were there in the packet?

Pink pencils	Red pencils	White pencils
2x8	3x8
	3x3	5x3
16 u	9 u	15 u

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

Remaining fraction of red pencils = ³₈
Remaining fraction of white pencils = 1 - ³₈ = ⁵₈

The total number of red pencils and white pencils is the repeated identity.
Make the repeated identity the same by using LCM.
LCM of 3 and 8 = 24

White pencils : Pink pencils
15 : 16

(b)
Difference in the number of pink pencils and red pencils
= 16 u - 9 u
= 7 u

7 u = 182
1 u = 182 ÷ 7 = 26

Total number of pencils
= 16 u + 9 u + 15 u
= 40 u
= 40 x 26
= 1040

Answer(s): (a) 15 : 16; (b) 1040