There are 20% as many red balls as green balls in Esther's collection of balls. The number of purple balls is 30% fewer than the number of green balls. There are 420 more purple balls than red balls.

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

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

(a)
20% = ²⁰₁₀₀ = ¹₅

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of green balls is the repeated identity. Make the number of green balls the same.  LCM of 5 and 10 is 10.

Number of more purple balls than red balls
= 7 u - 2 u
= 5 u

5 u = 420

1 u = 420 ÷ 5 = 84

Total number of balls in the collection
= 2 u + 10 u + 7 u 
= 19 u
= 19 x 84
= 1596

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

Answer(s): (a) 1596; (b) 142⁶₇ %