There are 25% as many blue beads as purple beads in Elyse's collection of beads. The number of white beads is 45% fewer than the number of purple beads. There are 360 more white beads than blue 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 white beads? Leave your answer as a mixed number in its simplest form.

Blue	Purple	White
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 white beads than blue beads
= 11 u - 5 u
= 6 u

6 u = 360

1 u = 360 ÷ 6 = 60

Total number of beads in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 60
= 2160

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

Answer(s): (a) 2160; (b) 181⁹₁₁ %