There are 25% as many red marbles as purple marbles in Betty's collection of marbles. The number of blue marbles is 45% fewer than the number of purple marbles. There are 504 more blue marbles than red marbles.

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

Red	Purple	Blue
1x5	4x5
	20x1	11x1
5 u	20 u	11 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more blue marbles than red marbles
= 11 u - 5 u
= 6 u

6 u = 504

1 u = 504 ÷ 6 = 84

Total number of marbles in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 84
= 3024

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

Answer(s): (a) 3024; (b) 181⁹₁₁ %