There are 25% as many purple balls as pink balls in Roshel's collection of balls. The number of yellow balls is 45% fewer than the number of pink balls. There are 438 more yellow balls than purple balls.

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

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

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

6 u = 438

1 u = 438 ÷ 6 = 73

Total number of balls in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 73
= 2628

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

Answer(s): (a) 2628; (b) 181⁹₁₁ %