There are 10% as many silver marbles as red marbles in Raeann's collection of marbles. The number of blue marbles is 40% fewer than the number of red marbles. There are 290 more blue marbles than silver marbles.

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

Silver	Red	Blue
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

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

Number of more blue marbles than silver marbles
= 6 u - 1 u
= 5 u

5 u = 290

1 u = 290 ÷ 5 = 58

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 58
= 986

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

Answer(s): (a) 986; (b) 166²₃ %