Jen had some green and blue marbles. If she gives away 38 green marbles, the number of green marbles will be 10% of the total number of marbles left. If she gives away 18 blue marbles, the number of green marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Green	Blue	Green	Blue
Before	1 u + 38	9 u	1 p	3 p + 18
Change	- 38	No change	No change	- 18
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 38 = 1 p --- (1)

9 u = 3 p + 18
9 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 114 = 3 p --- (3) 

(2) = (3)
9 u - 18 = 3 u + 114 
9 u - 3 u = 114 + 18
6 u = 132

1 u = 132 ÷ 6 = 22

Number of marbles that Jen had at first
= 1 u + 38 + 9 u
= 10 u + 38
= 10 x 22 + 38
= 220 + 38
= 258

(b)
Number of blue marbles
= 9 u
= 9 x 22
= 198

Fraction of Jen's marbles that is blue 
= ¹⁹⁸₂₅₈
= ³³₄₃

Answer(s): (a) 258; (b) ³³₄₃