There are 20% as many white marbles as blue marbles in Mary's collection of marbles. The number of black marbles is 30% fewer than the number of blue marbles. There are 445 more black marbles than white marbles.

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

White	Blue	Black
1x2	5x2
	10x1	7x1
2 u	10 u	7 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of blue marbles is the repeated identity. Make the number of blue marbles the same.  LCM of 5 and 10 is 10.

Number of more black marbles than white marbles
= 7 u - 2 u
= 5 u

5 u = 445

1 u = 445 ÷ 5 = 89

Total number of marbles in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 89
= 1691

(b)
Percentage of the number of blue marbles as compared to the number of black marbles
= ¹⁰₇ x 100%
= ¹⁰⁰⁰₇ %
= 142⁶₇ %

Answer(s): (a) 1691; (b) 142⁶₇ %