Cathy had some yellow and blue marbles. If she gives away 32 yellow marbles, the number of yellow marbles will be 10% of the total number of marbles left. If she gives away 18 blue marbles, the number of yellow marbles will be 25% of the total number of marbles left.

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

	Scenario 1		Scenario 2
	Yellow	Blue	Yellow	Blue
Before	1 u + 32	9 u	1 p	3 p + 18
Change	- 32	No change	No change	- 18
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 32 = 1 p --- (1)

9 u = 3 p + 18
9 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 96 = 3 p --- (3) 

(2) = (3)
9 u - 18 = 3 u + 96 
9 u - 3 u = 96 + 18
6 u = 114

1 u = 114 ÷ 6 = 19

Number of marbles that Cathy had at first
= 1 u + 32 + 9 u
= 10 u + 32
= 10 x 19 + 32
= 190 + 32
= 222

(b)
Number of blue marbles
= 9 u
= 9 x 19
= 171

Fraction of Cathy's marbles that is blue 
= ¹⁷¹₂₂₂
= ⁵⁷₇₄

Answer(s): (a) 222; (b) ⁵⁷₇₄