Victoria had some purple and grey marbles. If she gives away 14 purple marbles, the number of purple marbles will be 20% of the total number of marbles left. If she gives away 42 grey marbles, the number of purple marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Purple	Grey	Purple	Grey
Before	1 u + 14	4 u	1 p	3 p + 42
Change	- 14	No change	No change	- 42
After	1 u	4 u	1 p	3 p

(a)
20% = ²⁰₁₀₀ = ¹₅

25% = ²⁵₁₀₀ = ¹₄

1 u + 14 = 1 p --- (1)

4 u = 3 p + 42
4 u - 42 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 42 = 3 p --- (3) 

(2) = (3)
4 u - 42 = 3 u + 42 
4 u - 3 u = 42 + 42

1 u = 84

Number of marbles that Victoria had at first
= 1 u + 14 + 4 u
= 5 u + 14
= 5 x 84 + 14
= 420 + 14
= 434

(b)
Number of grey marbles
= 4 u
= 4 x 84
= 336

Fraction of Victoria's marbles that is grey 
= ³³⁶₄₃₄
= ²⁴₃₁

Answer(s): (a) 434; (b) ²⁴₃₁