There are 20% as many brown beads as grey beads in Shiyun's collection of beads. The number of green beads is 35% fewer than the number of grey beads. There are 513 more green beads than brown beads.

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

Brown	Grey	Green
1x4	5x4
	20x1	13x1
4 u	20 u	13 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

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

9 u = 513

1 u = 513 ÷ 9 = 57

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 57
= 2109

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

Answer(s): (a) 2109; (b) 153¹¹₁₃ %