There are 10% as many white marbles as pink marbles in Gillian's collection of marbles. The number of brown marbles is 45% fewer than the number of pink marbles. There are 306 more brown marbles than white marbles.

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

White	Pink	Brown
1x2	10x2
	20x1	11x1
2 u	20 u	11 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more brown marbles than white marbles
= 11 u - 2 u
= 9 u

9 u = 306

1 u = 306 ÷ 9 = 34

Total number of marbles in the collection
= 2 u + 20 u + 11 u 
= 33 u
= 33 x 34
= 1122

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

Answer(s): (a) 1122; (b) 181⁹₁₁ %