PSLE
A box contained purple and black beads. At first, the number of purple beads was ¹₃ the number of black beads. After ¹₂ of the purple beads and ⁷₁₂ of the black beads were used, 35 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?

	Purple	Black
Comparing purple beads and black beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	12x1 = 12 u
Change	- 1x2 =  - 2 u	- 7x1 = - 7 u
After	1x2 =  2 u	5x1 = 5 u

(a)
The number of black beads at first is repeated. Make the number of black beads at first the same. LCM of 3 and 12 is 12.

The number of purple beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 7}_{4 + 12} 
= ⁹₁₆

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

7 u = 35

1 u = 35 ÷ 7 = 5

Number of beads at first
= 16 u
= 16 x 5
= 80

Answer(s): (a) ⁹₁₆; (b) 80