Lynn had some black and gold marbles. If she gives away 40 black marbles, the number of black marbles will be 10% of the total number of marbles left. If she gives away 30 gold marbles, the number of black marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Black	Gold	Black	Gold
Before	1 u + 40	9 u	1 p	3 p + 30
Change	- 40	No change	No change	- 30
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 40 = 1 p --- (1)

9 u = 3 p + 30
9 u - 30 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 120 = 3 p --- (3) 

(2) = (3)
9 u - 30 = 3 u + 120 
9 u - 3 u = 120 + 30
6 u = 150

1 u = 150 ÷ 6 = 25

Number of marbles that Lynn had at first
= 1 u + 40 + 9 u
= 10 u + 40
= 10 x 25 + 40
= 250 + 40
= 290

(b)
Number of gold marbles
= 9 u
= 9 x 25
= 225

Fraction of Lynn's marbles that is gold 
= ²²⁵₂₉₀
= ⁴⁵₅₈

Answer(s): (a) 290; (b) ⁴⁵₅₈