There are 15% as many white beads as grey beads in Barbara's collection of beads. The number of yellow beads is 40% fewer than the number of grey beads. There are 432 more yellow beads than white 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.

White	Grey	Yellow
3x1	20x1
	5x4	3x4
3 u	20 u	12 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

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

Number of more yellow beads than white beads
= 12 u - 3 u
= 9 u

9 u = 432

1 u = 432 ÷ 9 = 48

Total number of beads in the collection
= 3 u + 20 u + 12 u 
= 35 u
= 35 x 48
= 1680

(b)
Percentage of the number of grey beads as compared to the number of yellow beads
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 1680; (b) 166²₃ %