There are 15% as many gold marbles as red marbles in Fiona's collection of marbles. The number of black marbles is 30% fewer than the number of red marbles. There are 484 more black marbles than gold 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 black marbles? Leave your answer as a mixed number in its simplest form.

Gold	Red	Black
3x1	20x1
	10x2	7x2
3 u	20 u	14 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

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 20 and 10 is 20.

Number of more black marbles than gold marbles
= 14 u - 3 u
= 11 u

11 u = 484

1 u = 484 ÷ 11 = 44

Total number of marbles in the collection
= 3 u + 20 u + 14 u 
= 37 u
= 37 x 44
= 1628

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

Answer(s): (a) 1628; (b) 142⁶₇ %