There are 25% as many pink balls as grey balls in Zara's collection of balls. The number of purple balls is 45% fewer than the number of grey balls. There are 456 more purple balls than pink 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 purple balls? Leave your answer as a mixed number in its simplest form.

Pink	Grey	Purple
1x5	4x5
	20x1	11x1
5 u	20 u	11 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

The number of grey balls is the repeated identity. Make the number of grey balls the same.  LCM of 4 and 20 is 20.

Number of more purple balls than pink balls
= 11 u - 5 u
= 6 u

6 u = 456

1 u = 456 ÷ 6 = 76

Total number of balls in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 76
= 2736

(b)
Percentage of the number of grey balls as compared to the number of purple balls
= ²⁰₁₁ x 100%
= ²⁰⁰⁰₁₁ %
= 181⁹₁₁ %

Answer(s): (a) 2736; (b) 181⁹₁₁ %