There are 25% as many blue marbles as red marbles in Jaslyn's collection of marbles. The number of purple marbles is 45% fewer than the number of red marbles. There are 252 more purple marbles than blue marbles.

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

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

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

6 u = 252

1 u = 252 ÷ 6 = 42

Total number of marbles in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 42
= 1512

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

Answer(s): (a) 1512; (b) 181⁹₁₁ %