There are 20% as many white marbles as green marbles in Cathy's collection of marbles. The number of grey marbles is 30% fewer than the number of green marbles. There are 285 more grey marbles than white marbles.

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

White	Green	Grey
1x2	5x2
	10x1	7x1
2 u	10 u	7 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

Number of more grey marbles than white marbles
= 7 u - 2 u
= 5 u

5 u = 285

1 u = 285 ÷ 5 = 57

Total number of marbles in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 57
= 1083

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

Answer(s): (a) 1083; (b) 142⁶₇ %