There are 10% as many red marbles as blue marbles in Opal's collection of marbles. The number of green marbles is 40% fewer than the number of blue marbles. There are 520 more green marbles than red 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 green marbles? Leave your answer as a mixed number in its simplest form.

Red	Blue	Green
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 green marbles than red marbles
= 6 u - 1 u
= 5 u

5 u = 520

1 u = 520 ÷ 5 = 104

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 104
= 1768

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

Answer(s): (a) 1768; (b) 166²₃ %