There are 20% as many blue marbles as white marbles in Yoko's collection of marbles. The number of yellow marbles is 45% fewer than the number of white marbles. There are 287 more yellow marbles than blue marbles.

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

Blue	White	Yellow
1x4	5x4
	20x1	11x1
4 u	20 u	11 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

7 u = 287

1 u = 287 ÷ 7 = 41

Total number of marbles in the collection
= 4 u + 20 u + 11 u 
= 35 u
= 35 x 41
= 1435

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

Answer(s): (a) 1435; (b) 181⁹₁₁ %