There are 10% as many yellow marbles as blue marbles in Vanessa's collection of marbles. The number of white marbles is 40% fewer than the number of blue marbles. There are 405 more white marbles than yellow marbles.

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

Yellow	Blue	White
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

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

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

5 u = 405

1 u = 405 ÷ 5 = 81

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 81
= 1377

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

Answer(s): (a) 1377; (b) 166²₃ %