Marion had some gold and blue marbles. If she gives away 24 gold marbles, the number of gold marbles will be 10% of the total number of marbles left. If she gives away 12 blue marbles, the number of gold marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Gold	Blue	Gold	Blue
Before	1 u + 24	9 u	1 p	3 p + 12
Change	- 24	No change	No change	- 12
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 + 12
9 u - 12 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 72 = 3 p --- (3) 

(2) = (3)
9 u - 12 = 3 u + 72 
9 u - 3 u = 72 + 12
6 u = 84

1 u = 84 ÷ 6 = 14

Number of marbles that Marion had at first
= 1 u + 24 + 9 u
= 10 u + 24
= 10 x 14 + 24
= 140 + 24
= 164

(b)
Number of blue marbles
= 9 u
= 9 x 14
= 126

Fraction of Marion's marbles that is blue 
= ¹²⁶₁₆₄
= ⁶³₈₂

Answer(s): (a) 164; (b) ⁶³₈₂