There are 20% as many yellow marbles as pink marbles in Cindy's collection of marbles. The number of grey marbles is 35% fewer than the number of pink marbles. There are 423 more grey marbles than yellow marbles.

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

Yellow	Pink	Grey
1x4	5x4
	20x1	13x1
4 u	20 u	13 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

Number of more grey marbles than yellow marbles
= 13 u - 4 u
= 9 u

9 u = 423

1 u = 423 ÷ 9 = 47

Total number of marbles in the collection
= 4 u + 20 u + 13 u 
= 37 u
= 37 x 47
= 1739

(b)
Percentage of the number of pink marbles as compared to the number of grey marbles
= ²⁰₁₃ x 100%
= ²⁰⁰⁰₁₃ %
= 153¹¹₁₃ %

Answer(s): (a) 1739; (b) 153¹¹₁₃ %