There are 20% as many purple marbles as silver marbles in Esther's collection of marbles. The number of white marbles is 45% fewer than the number of silver marbles. There are 252 more white marbles than purple marbles.

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

Purple	Silver	White
1x4	5x4
	20x1	11x1
4 u	20 u	11 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

Number of more white marbles than purple marbles
= 11 u - 4 u
= 7 u

7 u = 252

1 u = 252 ÷ 7 = 36

Total number of marbles in the collection
= 4 u + 20 u + 11 u 
= 35 u
= 35 x 36
= 1260

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

Answer(s): (a) 1260; (b) 181⁹₁₁ %