PSLE
A box contained blue and orange beads. At first, the number of blue beads was ¹₃ the number of orange beads. After ²₅ of the blue beads and ⁹₁₀ of the orange beads were used, 54 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Blue	Orange
Comparing blue beads and orange beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 2x2 =  - 4 u	- 9x3 = - 27 u
After	3x2 =  6 u	1x3 = 3 u

(a)
The number of orange beads at first is repeated. Make the number of orange beads at first the same. LCM of 3 and 10 is 30.

The number of blue beads at first is repeated.

Since the number of blue beads at first is 10 u, we make the total number of blue beads at first the same by multiplying 5 by 2 to become 10 u too.

Fraction of the beads used
= ^{4 + 27}_{10 + 30} 
= ³¹₄₀

(b)
Number of beads left
= 6 u + 3 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of beads at first
= 40 u
= 40 x 6
= 240

Answer(s): (a) ³¹₄₀; (b) 240