There are 10% as many grey marbles as white marbles in Kimberly's collection of marbles. The number of blue marbles is 45% fewer than the number of white marbles. There are 288 more blue marbles than grey marbles.

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

Grey	White	Blue
1x2	10x2
	20x1	11x1
2 u	20 u	11 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

The number of white marbles is the repeated identity. Make the number of white marbles the same.  LCM of 10 and 20 is 20.

Number of more blue marbles than grey marbles
= 11 u - 2 u
= 9 u

9 u = 288

1 u = 288 ÷ 9 = 32

Total number of marbles in the collection
= 2 u + 20 u + 11 u 
= 33 u
= 33 x 32
= 1056

(b)
Percentage of the number of white marbles as compared to the number of blue marbles
= ²⁰₁₁ x 100%
= ²⁰⁰⁰₁₁ %
= 181⁹₁₁ %

Answer(s): (a) 1056; (b) 181⁹₁₁ %