Kimberly had some blue and purple balls. If she gives away 50 blue balls, the number of blue balls will be 10% of the total number of balls left. If she gives away 18 purple balls, the number of blue balls will be 25% of the total number of balls left.

1. How many balls does Kimberly have altogether?
2. What fraction of Kimberly's balls is purple?

	Scenario 1		Scenario 2
	Blue	Purple	Blue	Purple
Before	1 u + 50	9 u	1 p	3 p + 18
Change	- 50	No change	No change	- 18
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 50 = 1 p --- (1)

9 u = 3 p + 18
9 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 150 = 3 p --- (3) 

(2) = (3)
9 u - 18 = 3 u + 150 
9 u - 3 u = 150 + 18
6 u = 168

1 u = 168 ÷ 6 = 28

Number of balls that Kimberly had at first
= 1 u + 50 + 9 u
= 10 u + 50
= 10 x 28 + 50
= 280 + 50
= 330

(b)
Number of purple balls
= 9 u
= 9 x 28
= 252

Fraction of Kimberly's balls that is purple 
= ²⁵²₃₃₀
= ⁴²₅₅

Answer(s): (a) 330; (b) ⁴²₅₅