There are 25% as many green balls as purple balls in Cindy's collection of balls. The number of brown balls is 45% fewer than the number of purple balls. There are 348 more brown balls than green 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 brown balls? Leave your answer as a mixed number in its simplest form.

Green	Purple	Brown
1x5	4x5
	20x1	11x1
5 u	20 u	11 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more brown balls than green balls
= 11 u - 5 u
= 6 u

6 u = 348

1 u = 348 ÷ 6 = 58

Total number of balls in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 58
= 2088

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

Answer(s): (a) 2088; (b) 181⁹₁₁ %