There are 20% as many brown beads as purple beads in Pamela's collection of beads. The number of grey beads is 35% fewer than the number of purple beads. There are 351 more grey beads than brown beads.

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

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

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

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

9 u = 351

1 u = 351 ÷ 9 = 39

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 39
= 1443

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

Answer(s): (a) 1443; (b) 153¹¹₁₃ %