Fiona had some gold and pink marbles. If she gives away 11 gold marbles, the number of gold marbles will be 10% of the total number of marbles left. If she gives away 45 pink marbles, the number of gold marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Gold	Pink	Gold	Pink
Before	1 u + 11	9 u	1 p	3 p + 45
Change	- 11	No change	No change	- 45
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 11 = 1 p --- (1)

9 u = 3 p + 45
9 u - 45 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 33 = 3 p --- (3) 

(2) = (3)
9 u - 45 = 3 u + 33 
9 u - 3 u = 33 + 45
6 u = 78

1 u = 78 ÷ 6 = 13

Number of marbles that Fiona had at first
= 1 u + 11 + 9 u
= 10 u + 11
= 10 x 13 + 11
= 130 + 11
= 141

(b)
Number of pink marbles
= 9 u
= 9 x 13
= 117

Fraction of Fiona's marbles that is pink 
= ¹¹⁷₁₄₁
= ³⁹₄₇

Answer(s): (a) 141; (b) ³⁹₄₇