There are 15% as many black marbles as gold marbles in Xuan's collection of marbles. The number of green marbles is 30% fewer than the number of gold marbles. There are 385 more green marbles than black marbles.

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

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

(a)
15% = ¹⁵₁₀₀ = ³₂₀

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of gold marbles is the repeated identity. Make the number of gold marbles the same.  LCM of 20 and 10 is 20.

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

11 u = 385

1 u = 385 ÷ 11 = 35

Total number of marbles in the collection
= 3 u + 20 u + 14 u 
= 37 u
= 37 x 35
= 1295

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

Answer(s): (a) 1295; (b) 142⁶₇ %