There are 10% as many yellow balls as purple balls in Raeann's collection of balls. The number of grey balls is 40% fewer than the number of purple balls. There are 450 more grey balls than yellow balls.

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

Yellow	Purple	Grey
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of purple balls is the repeated identity. Make the number of purple balls the same.  LCM of 10 and 5 is 10.

Number of more grey balls than yellow balls
= 6 u - 1 u
= 5 u

5 u = 450

1 u = 450 ÷ 5 = 90

Total number of balls in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 90
= 1530

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

Answer(s): (a) 1530; (b) 166²₃ %