There are 20% as many yellow marbles as green marbles in Sarah's collection of marbles. The number of gold marbles is 45% fewer than the number of green marbles. There are 322 more gold marbles than yellow 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 gold marbles? Leave your answer as a mixed number in its simplest form.

Yellow	Green	Gold
1x4	5x4
	20x1	11x1
4 u	20 u	11 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

7 u = 322

1 u = 322 ÷ 7 = 46

Total number of marbles in the collection
= 4 u + 20 u + 11 u 
= 35 u
= 35 x 46
= 1610

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

Answer(s): (a) 1610; (b) 181⁹₁₁ %