Kimberly had some grey and gold marbles. If she gives away 14 grey marbles, the number of grey marbles will be 10% of the total number of marbles left. If she gives away 18 gold marbles, the number of grey marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Grey	Gold	Grey	Gold
Before	1 u + 14	9 u	1 p	3 p + 18
Change	- 14	No change	No change	- 18
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 14 = 1 p --- (1)

9 u = 3 p + 18
9 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 42 = 3 p --- (3) 

(2) = (3)
9 u - 18 = 3 u + 42 
9 u - 3 u = 42 + 18
6 u = 60

1 u = 60 ÷ 6 = 10

Number of marbles that Kimberly had at first
= 1 u + 14 + 9 u
= 10 u + 14
= 10 x 10 + 14
= 100 + 14
= 114

(b)
Number of gold marbles
= 9 u
= 9 x 10
= 90

Fraction of Kimberly's marbles that is gold 
= ⁹⁰₁₁₄
= ¹⁵₁₉

Answer(s): (a) 114; (b) ¹⁵₁₉