Min had some blue and black marbles. If she gives away 25 blue marbles, the number of blue marbles will be 10% of the total number of marbles left. If she gives away 15 black marbles, the number of blue marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Blue	Black	Blue	Black
Before	1 u + 25	9 u	1 p	3 p + 15
Change	- 25	No change	No change	- 15
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 25 = 1 p --- (1)

9 u = 3 p + 15
9 u - 15 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 75 = 3 p --- (3) 

(2) = (3)
9 u - 15 = 3 u + 75 
9 u - 3 u = 75 + 15
6 u = 90

1 u = 90 ÷ 6 = 15

Number of marbles that Min had at first
= 1 u + 25 + 9 u
= 10 u + 25
= 10 x 15 + 25
= 150 + 25
= 175

(b)
Number of black marbles
= 9 u
= 9 x 15
= 135

Fraction of Min's marbles that is black 
= ¹³⁵₁₇₅
= ²⁷₃₅

Answer(s): (a) 175; (b) ²⁷₃₅