Eva had some silver and purple marbles. If she gives away 45 silver marbles, the number of silver marbles will be 20% of the total number of marbles left. If she gives away 30 purple marbles, the number of silver marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Silver	Purple	Silver	Purple
Before	1 u + 45	4 u	1 p	3 p + 30
Change	- 45	No change	No change	- 30
After	1 u	4 u	1 p	3 p

(a)
20% = ²⁰₁₀₀ = ¹₅

25% = ²⁵₁₀₀ = ¹₄

1 u + 45 = 1 p --- (1)

4 u = 3 p + 30
4 u - 30 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 135 = 3 p --- (3) 

(2) = (3)
4 u - 30 = 3 u + 135 
4 u - 3 u = 135 + 30

1 u = 165

Number of marbles that Eva had at first
= 1 u + 45 + 4 u
= 5 u + 45
= 5 x 165 + 45
= 825 + 45
= 870

(b)
Number of purple marbles
= 4 u
= 4 x 165
= 660

Fraction of Eva's marbles that is purple 
= ⁶⁶⁰₈₇₀
= ²²₂₉

Answer(s): (a) 870; (b) ²²₂₉