There are 10% as many green marbles as red marbles in Cathy's collection of marbles. The number of gold marbles is 40% fewer than the number of red marbles. There are 265 more gold marbles than green 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 gold marbles? Leave your answer as a mixed number in its simplest form.

Green	Red	Gold
1x1	10x1
	5x2	3x2
1 u	10 u	6 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

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

Number of more gold marbles than green marbles
= 6 u - 1 u
= 5 u

5 u = 265

1 u = 265 ÷ 5 = 53

Total number of marbles in the collection
= 1 u + 10 u + 6 u 
= 17 u
= 17 x 53
= 901

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

Answer(s): (a) 901; (b) 166²₃ %