Fiona had some blue and yellow marbles. If she gives away 43 blue marbles, the number of blue marbles will be 10% of the total number of marbles left. If she gives away 45 yellow marbles, the number of blue 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 yellow?

	Scenario 1		Scenario 2
	Blue	Yellow	Blue	Yellow
Before	1 u + 43	9 u	1 p	3 p + 45
Change	- 43	No change	No change	- 45
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 43 = 1 p --- (1)

9 u = 3 p + 45
9 u - 45 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 129 = 3 p --- (3) 

(2) = (3)
9 u - 45 = 3 u + 129 
9 u - 3 u = 129 + 45
6 u = 174

1 u = 174 ÷ 6 = 29

Number of marbles that Fiona had at first
= 1 u + 43 + 9 u
= 10 u + 43
= 10 x 29 + 43
= 290 + 43
= 333

(b)
Number of yellow marbles
= 9 u
= 9 x 29
= 261

Fraction of Fiona's marbles that is yellow 
= ²⁶¹₃₃₃
= ²⁹₃₇

Answer(s): (a) 333; (b) ²⁹₃₇