Vanessa had some purple and blue marbles. If she gives away 28 purple marbles, the number of purple marbles will be 10% of the total number of marbles left. If she gives away 12 blue marbles, the number of purple marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Purple	Blue	Purple	Blue
Before	1 u + 28	9 u	1 p	3 p + 12
Change	- 28	No change	No change	- 12
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 28 = 1 p --- (1)

9 u = 3 p + 12
9 u - 12 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 84 = 3 p --- (3) 

(2) = (3)
9 u - 12 = 3 u + 84 
9 u - 3 u = 84 + 12
6 u = 96

1 u = 96 ÷ 6 = 16

Number of marbles that Vanessa had at first
= 1 u + 28 + 9 u
= 10 u + 28
= 10 x 16 + 28
= 160 + 28
= 188

(b)
Number of blue marbles
= 9 u
= 9 x 16
= 144

Fraction of Vanessa's marbles that is blue 
= ¹⁴⁴₁₈₈
= ³⁶₄₇

Answer(s): (a) 188; (b) ³⁶₄₇