Emily had some pink and black marbles. If she gives away 37 pink marbles, the number of pink marbles will be 10% of the total number of marbles left. If she gives away 45 black marbles, the number of pink marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Pink	Black	Pink	Black
Before	1 u + 37	9 u	1 p	3 p + 45
Change	- 37	No change	No change	- 45
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 37 = 1 p --- (1)

9 u = 3 p + 45
9 u - 45 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 111 = 3 p --- (3) 

(2) = (3)
9 u - 45 = 3 u + 111 
9 u - 3 u = 111 + 45
6 u = 156

1 u = 156 ÷ 6 = 26

Number of marbles that Emily had at first
= 1 u + 37 + 9 u
= 10 u + 37
= 10 x 26 + 37
= 260 + 37
= 297

(b)
Number of black marbles
= 9 u
= 9 x 26
= 234

Fraction of Emily's marbles that is black 
= ²³⁴₂₉₇
= ²⁶₃₃

Answer(s): (a) 297; (b) ²⁶₃₃