Shannon had some grey and black marbles. If she gives away 48 grey marbles, the number of grey marbles will be 10% of the total number of marbles left. If she gives away 24 black marbles, the number of grey marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Grey	Black	Grey	Black
Before	1 u + 48	9 u	1 p	3 p + 24
Change	- 48	No change	No change	- 24
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 48 = 1 p --- (1)

9 u = 3 p + 24
9 u - 24 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 144 = 3 p --- (3) 

(2) = (3)
9 u - 24 = 3 u + 144 
9 u - 3 u = 144 + 24
6 u = 168

1 u = 168 ÷ 6 = 28

Number of marbles that Shannon had at first
= 1 u + 48 + 9 u
= 10 u + 48
= 10 x 28 + 48
= 280 + 48
= 328

(b)
Number of black marbles
= 9 u
= 9 x 28
= 252

Fraction of Shannon's marbles that is black 
= ²⁵²₃₂₈
= ⁶³₈₂

Answer(s): (a) 328; (b) ⁶³₈₂