There are 10% as many yellow balls as purple balls in Xuan's collection of balls. The number of white balls is 35% fewer than the number of purple balls. There are 484 more white balls than yellow balls.

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

Yellow	Purple	White
1x2	10x2
	20x1	13x1
2 u	20 u	13 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

100% - 35% = 65%
65% = ⁶⁵₁₀₀ = ¹³₂₀

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

Number of more white balls than yellow balls
= 13 u - 2 u
= 11 u

11 u = 484

1 u = 484 ÷ 11 = 44

Total number of balls in the collection
= 2 u + 20 u + 13 u 
= 35 u
= 35 x 44
= 1540

(b)
Percentage of the number of purple balls as compared to the number of white balls
= ²⁰₁₃ x 100%
= ²⁰⁰⁰₁₃ %
= 153¹¹₁₃ %

Answer(s): (a) 1540; (b) 153¹¹₁₃ %