There are 25% as many yellow balls as grey balls in Linda's collection of balls. The number of purple balls is 30% fewer than the number of grey balls. There are 540 more purple balls than yellow balls.

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

Yellow	Grey	Purple
1x5	4x5
	10x2	7x2
5 u	20 u	14 u

(a)
25% = ²⁵₁₀₀ = ¹₄

100% - 30% = 70%
70% = ⁷⁰₁₀₀ = ⁷₁₀

The number of grey balls is the repeated identity. Make the number of grey balls the same.  LCM of 4 and 10 is 20.

Number of more purple balls than yellow balls
= 14 u - 5 u
= 9 u

9 u = 540

1 u = 540 ÷ 9 = 60

Total number of balls in the collection
= 5 u + 20 u + 14 u 
= 39 u
= 39 x 60
= 2340

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

Answer(s): (a) 2340; (b) 142⁶₇ %