There are 20% as many blue marbles as red marbles in Gem's collection of marbles. The number of white marbles is 45% fewer than the number of red marbles. There are 448 more white marbles than blue marbles.

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

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

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 45% = 55%
55% = ⁵⁵₁₀₀ = ¹¹₂₀

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

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

7 u = 448

1 u = 448 ÷ 7 = 64

Total number of marbles in the collection
= 4 u + 20 u + 11 u 
= 35 u
= 35 x 64
= 2240

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

Answer(s): (a) 2240; (b) 181⁹₁₁ %