There are 15% as many pink balls as black balls in Lucy's collection of balls. The number of brown balls is 40% fewer than the number of black balls. There are 315 more brown balls than pink balls.

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

Pink	Black	Brown
3x1	20x1
	5x4	3x4
3 u	20 u	12 u

(a)
15% = ¹⁵₁₀₀ = ³₂₀

100% - 40% = 60%
60% = ⁶⁰₁₀₀ = ³₅

The number of black balls is the repeated identity. Make the number of black balls the same.  LCM of 20 and 5 is 20.

Number of more brown balls than pink balls
= 12 u - 3 u
= 9 u

9 u = 315

1 u = 315 ÷ 9 = 35

Total number of balls in the collection
= 3 u + 20 u + 12 u 
= 35 u
= 35 x 35
= 1225

(b)
Percentage of the number of black balls as compared to the number of brown balls
= ⁵₃ x 100%
= ⁵⁰⁰₃ %
= 166²₃ %

Answer(s): (a) 1225; (b) 166²₃ %