There are 15% as many gold marbles as purple marbles in Joelle's collection of marbles. The number of silver marbles is 40% fewer than the number of purple marbles. There are 351 more silver marbles than gold 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 silver marbles? Leave your answer as a mixed number in its simplest form.

Gold	Purple	Silver
3x1	20x1
	5x4	3x4
3 u	20 u	12 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

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 20 and 5 is 20.

Number of more silver marbles than gold marbles
= 12 u - 3 u
= 9 u

9 u = 351

1 u = 351 ÷ 9 = 39

Total number of marbles in the collection
= 3 u + 20 u + 12 u 
= 35 u
= 35 x 39
= 1365

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

Answer(s): (a) 1365; (b) 166²₃ %