There are 20% as many green beads as grey beads in Emma's collection of beads. The number of yellow beads is 35% fewer than the number of grey beads. There are 432 more yellow beads than green 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 yellow beads? Leave your answer as a mixed number in its simplest form.

Green	Grey	Yellow
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 yellow beads than green beads
= 13 u - 4 u
= 9 u

9 u = 432

1 u = 432 ÷ 9 = 48

Total number of beads in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 48
= 1776

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

Answer(s): (a) 1776; (b) 153¹¹₁₃ %