There are 10% as many white marbles as purple marbles in Vanessa's collection of marbles. The number of brown marbles is 40% fewer than the number of purple marbles. There are 300 more brown marbles than white marbles.

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

White	Purple	Brown
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of purple marbles is the repeated identity. Make the number of purple marbles the same.  LCM of 10 and 5 is 10.

Number of more brown marbles than white marbles
= 6 u - 1 u
= 5 u

5 u = 300

1 u = 300 ÷ 5 = 60

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 60
= 1020

(b)
Percentage of the number of purple marbles as compared to the number of brown marbles
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 1020; (b) 166²₃ %