There are 20% as many blue marbles as grey marbles in Joelle's collection of marbles. The number of gold marbles is 45% fewer than the number of grey marbles. There are 476 more gold marbles than blue marbles.

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

Blue	Grey	Gold
1x4	5x4
	20x1	11x1
4 u	20 u	11 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

The number of grey marbles is the repeated identity. Make the number of grey marbles the same.  LCM of 5 and 20 is 20.

Number of more gold marbles than blue marbles
= 11 u - 4 u
= 7 u

7 u = 476

1 u = 476 ÷ 7 = 68

Total number of marbles in the collection
= 4 u + 20 u + 11 u 
= 35 u
= 35 x 68
= 2380

(b)
Percentage of the number of grey marbles as compared to the number of gold marbles
= ²⁰₁₁ x 100%
= ²⁰⁰⁰₁₁ %
= 181⁹₁₁ %

Answer(s): (a) 2380; (b) 181⁹₁₁ %