Betty had some purple and green marbles. If she gives away 39 purple marbles, the number of purple marbles will be 20% of the total number of marbles left. If she gives away 36 green marbles, the number of purple marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Purple	Green	Purple	Green
Before	1 u + 39	4 u	1 p	3 p + 36
Change	- 39	No change	No change	- 36
After	1 u	4 u	1 p	3 p

(a)
20% = ²⁰₁₀₀ = ¹₅

25% = ²⁵₁₀₀ = ¹₄

1 u + 39 = 1 p --- (1)

4 u = 3 p + 36
4 u - 36 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 117 = 3 p --- (3) 

(2) = (3)
4 u - 36 = 3 u + 117 
4 u - 3 u = 117 + 36

1 u = 153

Number of marbles that Betty had at first
= 1 u + 39 + 4 u
= 5 u + 39
= 5 x 153 + 39
= 765 + 39
= 804

(b)
Number of green marbles
= 4 u
= 4 x 153
= 612

Fraction of Betty's marbles that is green 
= ⁶¹²₈₀₄
= ⁵¹₆₇

Answer(s): (a) 804; (b) ⁵¹₆₇