There are 10% as many purple marbles as silver marbles in Linda's collection of marbles. The number of black marbles is 40% fewer than the number of silver marbles. There are 495 more black marbles than purple marbles.

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

Purple	Silver	Black
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

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

Number of more black marbles than purple marbles
= 6 u - 1 u
= 5 u

5 u = 495

1 u = 495 ÷ 5 = 99

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 99
= 1683

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

Answer(s): (a) 1683; (b) 166²₃ %