There are 20% as many silver beads as black beads in Lynn's collection of beads. The number of brown beads is 35% fewer than the number of black beads. There are 477 more brown beads than silver 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 brown beads? Leave your answer as a mixed number in its simplest form.

Silver	Black	Brown
1x4	5x4
	20x1	13x1
4 u	20 u	13 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

The number of black beads is the repeated identity. Make the number of black beads the same.  LCM of 5 and 20 is 20.

Number of more brown beads than silver beads
= 13 u - 4 u
= 9 u

9 u = 477

1 u = 477 ÷ 9 = 53

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 53
= 1961

(b)
Percentage of the number of black beads as compared to the number of brown beads
= ²⁰₁₃ x 100%
= ²⁰⁰⁰₁₃ %
= 153¹¹₁₃ %

Answer(s): (a) 1961; (b) 153¹¹₁₃ %