There are 15% as many blue balls as grey balls in Natalie's collection of balls. The number of white balls is 40% fewer than the number of grey balls. There are 423 more white balls than blue balls.

1. Find the total number of balls in the collection.
2. What percentage are the number of grey balls as compared to the number of white balls? Leave your answer as a mixed number in its simplest form.

Blue	Grey	White
3x1	20x1
	5x4	3x4
3 u	20 u	12 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of grey balls is the repeated identity. Make the number of grey balls the same.  LCM of 20 and 5 is 20.

Number of more white balls than blue balls
= 12 u - 3 u
= 9 u

9 u = 423

1 u = 423 ÷ 9 = 47

Total number of balls in the collection
= 3 u + 20 u + 12 u 
= 35 u
= 35 x 47
= 1645

(b)
Percentage of the number of grey balls as compared to the number of white balls
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 1645; (b) 166²₃ %