There are 25% as many green beads as black beads in Min's collection of beads. The number of purple beads is 45% fewer than the number of black beads. There are 366 more purple beads than green beads.

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

Green	Black	Purple
1x5	4x5
	20x1	11x1
5 u	20 u	11 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more purple beads than green beads
= 11 u - 5 u
= 6 u

6 u = 366

1 u = 366 ÷ 6 = 61

Total number of beads in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 61
= 2196

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

Answer(s): (a) 2196; (b) 181⁹₁₁ %