There are 10% as many grey beads as white beads in Nicole's collection of beads. The number of black beads is 40% fewer than the number of white beads. There are 540 more black beads than grey beads.

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

Grey	White	Black
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of white beads is the repeated identity. Make the number of white beads the same.  LCM of 10 and 5 is 10.

Number of more black beads than grey beads
= 6 u - 1 u
= 5 u

5 u = 540

1 u = 540 ÷ 5 = 108

Total number of beads in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 108
= 1836

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

Answer(s): (a) 1836; (b) 166²₃ %