There are 25% as many pink beads as purple beads in Joelle's collection of beads. The number of silver beads is 45% fewer than the number of purple beads. There are 414 more silver beads than pink beads.

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

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

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more silver beads than pink beads
= 11 u - 5 u
= 6 u

6 u = 414

1 u = 414 ÷ 6 = 69

Total number of beads in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 69
= 2484

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

Answer(s): (a) 2484; (b) 181⁹₁₁ %