Xuan had some brown and pink marbles. If she gives away 24 brown marbles, the number of brown marbles will be 10% of the total number of marbles left. If she gives away 48 pink marbles, the number of brown marbles will be 25% of the total number of marbles left.

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

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

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 24 = 1 p --- (1)

9 u = 3 p + 48
9 u - 48 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 72 = 3 p --- (3) 

(2) = (3)
9 u - 48 = 3 u + 72 
9 u - 3 u = 72 + 48
6 u = 120

1 u = 120 ÷ 6 = 20

Number of marbles that Xuan had at first
= 1 u + 24 + 9 u
= 10 u + 24
= 10 x 20 + 24
= 200 + 24
= 224

(b)
Number of pink marbles
= 9 u
= 9 x 20
= 180

Fraction of Xuan's marbles that is pink 
= ¹⁸⁰₂₂₄
= ⁴⁵₅₆

Answer(s): (a) 224; (b) ⁴⁵₅₆