Raeann had some silver and brown beads. If she gives away 48 silver beads, the number of silver beads will be 10% of the total number of beads left. If she gives away 48 brown beads, the number of silver beads will be 25% of the total number of beads left.

1. How many beads does Raeann have altogether?
2. What fraction of Raeann's beads is brown?

	Scenario 1		Scenario 2
	Silver	Brown	Silver	Brown
Before	1 u + 48	9 u	1 p	3 p + 48
Change	- 48	No change	No change	- 48
After	1 u	9 u	1 p	3 p

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

25% = ²⁵₁₀₀ = ¹₄

1 u + 48 = 1 p --- (1)

9 u = 3 p + 48
9 u - 48 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 144 = 3 p --- (3) 

(2) = (3)
9 u - 48 = 3 u + 144 
9 u - 3 u = 144 + 48
6 u = 192

1 u = 192 ÷ 6 = 32

Number of beads that Raeann had at first
= 1 u + 48 + 9 u
= 10 u + 48
= 10 x 32 + 48
= 320 + 48
= 368

(b)
Number of brown beads
= 9 u
= 9 x 32
= 288

Fraction of Raeann's beads that is brown 
= ²⁸⁸₃₆₈
= ¹⁸₂₃

Answer(s): (a) 368; (b) ¹⁸₂₃