Yoko had some grey and white marbles. If she gives away 21 grey marbles, the number of grey marbles will be 10% of the total number of marbles left. If she gives away 27 white marbles, the number of grey marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Grey	White	Grey	White
Before	1 u + 21	9 u	1 p	3 p + 27
Change	- 21	No change	No change	- 27
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 21 = 1 p --- (1)

9 u = 3 p + 27
9 u - 27 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 63 = 3 p --- (3) 

(2) = (3)
9 u - 27 = 3 u + 63 
9 u - 3 u = 63 + 27
6 u = 90

1 u = 90 ÷ 6 = 15

Number of marbles that Yoko had at first
= 1 u + 21 + 9 u
= 10 u + 21
= 10 x 15 + 21
= 150 + 21
= 171

(b)
Number of white marbles
= 9 u
= 9 x 15
= 135

Fraction of Yoko's marbles that is white 
= ¹³⁵₁₇₁
= ¹⁵₁₉

Answer(s): (a) 171; (b) ¹⁵₁₉