There are 20% as many yellow beads as black beads in Marion's collection of beads. The number of silver beads is 35% fewer than the number of black beads. There are 540 more silver beads than yellow 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.

Yellow	Black	Silver
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 silver beads than yellow beads
= 13 u - 4 u
= 9 u

9 u = 540

1 u = 540 ÷ 9 = 60

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 60
= 2220

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

Answer(s): (a) 2220; (b) 153¹¹₁₃ %