There are 25% as many red marbles as pink marbles in Gem's collection of marbles. The number of purple marbles is 45% fewer than the number of pink marbles. There are 384 more purple marbles than red marbles.

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

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

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

6 u = 384

1 u = 384 ÷ 6 = 64

Total number of marbles in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 64
= 2304

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

Answer(s): (a) 2304; (b) 181⁹₁₁ %