Natalie had some purple and grey balls. If she gives away 49 purple balls, the number of purple balls will be 10% of the total number of balls left. If she gives away 45 grey balls, the number of purple balls will be 25% of the total number of balls left.

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

	Scenario 1		Scenario 2
	Purple	Grey	Purple	Grey
Before	1 u + 49	9 u	1 p	3 p + 45
Change	- 49	No change	No change	- 45
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 49 = 1 p --- (1)

9 u = 3 p + 45
9 u - 45 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 147 = 3 p --- (3) 

(2) = (3)
9 u - 45 = 3 u + 147 
9 u - 3 u = 147 + 45
6 u = 192

1 u = 192 ÷ 6 = 32

Number of balls that Natalie had at first
= 1 u + 49 + 9 u
= 10 u + 49
= 10 x 32 + 49
= 320 + 49
= 369

(b)
Number of grey balls
= 9 u
= 9 x 32
= 288

Fraction of Natalie's balls that is grey 
= ²⁸⁸₃₆₉
= ³²₄₁

Answer(s): (a) 369; (b) ³²₄₁