PSLE
A box contained blue and orange beads. At first, the number of blue beads was ¹₅ the number of orange beads. After ¹₂ of the blue beads and ³₄ of the orange beads were used, 49 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	1x4 = 4 u	5x4 = 20 u
Before	2x2 = 4 u	4x5 = 20 u
Change	- 1x2 =  - 2 u	- 3x5 = - 15 u
After	1x2 =  2 u	1x5 = 5 u

(a)
The number of orange beads at first is repeated. Make the number of orange beads at first the same. LCM of 5 and 4 is 20.

The number of blue beads at first is repeated.

Since the number of blue beads at first is 4 u, we make the total number of blue beads at first the same by multiplying 2 by 2 to become 4 u too.

Fraction of the beads used
= ^{2 + 15}_{4 + 20} 
= ¹⁷₂₄

(b)
Number of beads left
= 2 u + 5 u
= 7 u

7 u = 49

1 u = 49 ÷ 7 = 7

Number of beads at first
= 24 u
= 24 x 7
= 168

Answer(s): (a) ¹⁷₂₄; (b) 168