There are 20% as many red marbles as brown marbles in Xuan's collection of marbles. The number of green marbles is 30% fewer than the number of brown marbles. There are 400 more green marbles than red marbles.

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

Red	Brown	Green
1x2	5x2
	10x1	7x1
2 u	10 u	7 u

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

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

Number of more green marbles than red marbles
= 7 u - 2 u
= 5 u

5 u = 400

1 u = 400 ÷ 5 = 80

Total number of marbles in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 80
= 1520

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

Answer(s): (a) 1520; (b) 142⁶₇ %