There are 20% as many black marbles as red marbles in Vanessa's collection of marbles. The number of silver marbles is 30% fewer than the number of red marbles. There are 530 more silver marbles than black 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 silver marbles? Leave your answer as a mixed number in its simplest form.

Black	Red	Silver
1x2	5x2
	10x1	7x1
2 u	10 u	7 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

Number of more silver marbles than black marbles
= 7 u - 2 u
= 5 u

5 u = 530

1 u = 530 ÷ 5 = 106

Total number of marbles in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 106
= 2014

(b)
Percentage of the number of red marbles as compared to the number of silver marbles
= ¹⁰₇ x 100%
= ¹⁰⁰⁰₇ %
= 142⁶₇ %

Answer(s): (a) 2014; (b) 142⁶₇ %