There are 15% as many red marbles as black marbles in Jane's collection of marbles. The number of green marbles is 30% fewer than the number of black marbles. There are 451 more green marbles than red marbles.

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

Red	Black	Green
3x1	20x1
	10x2	7x2
3 u	20 u	14 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of black marbles is the repeated identity. Make the number of black marbles the same.  LCM of 20 and 10 is 20.

Number of more green marbles than red marbles
= 14 u - 3 u
= 11 u

11 u = 451

1 u = 451 ÷ 11 = 41

Total number of marbles in the collection
= 3 u + 20 u + 14 u 
= 37 u
= 37 x 41
= 1517

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

Answer(s): (a) 1517; (b) 142⁶₇ %