There are 25% as many red marbles as purple marbles in Emily's collection of marbles. The number of white marbles is 40% fewer than the number of purple marbles. There are 441 more white 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 white marbles? Leave your answer as a mixed number in its simplest form.

Red	Purple	White
1x5	4x5
	5x4	3x4
5 u	20 u	12 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of purple marbles is the repeated identity. Make the number of purple marbles the same.  LCM of 4 and 5 is 20.

Number of more white marbles than red marbles
= 12 u - 5 u
= 7 u

7 u = 441

1 u = 441 ÷ 7 = 63

Total number of marbles in the collection
= 5 u + 20 u + 12 u 
= 37 u
= 37 x 63
= 2331

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

Answer(s): (a) 2331; (b) 166²₃ %