There are 25% as many pink beads as black beads in Vanessa's collection of beads. The number of silver beads is 45% fewer than the number of black beads. There are 342 more silver beads than pink 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 silver beads? Leave your answer as a mixed number in its simplest form.

Pink	Black	Silver
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 silver beads than pink beads
= 11 u - 5 u
= 6 u

6 u = 342

1 u = 342 ÷ 6 = 57

Total number of beads in the collection
= 5 u + 20 u + 11 u 
= 36 u
= 36 x 57
= 2052

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

Answer(s): (a) 2052; (b) 181⁹₁₁ %