PSLE
A box contained purple and gold beads. At first, the number of purple beads was ¹₃ the number of gold beads. After ¹₂ of the purple beads and ³₄ of the gold beads were used, 15 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	Gold
Comparing purple beads and gold beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	4x3 = 12 u
Change	- 1x2 =  - 2 u	- 3x3 = - 9 u
After	1x2 =  2 u	1x3 = 3 u

(a)
The number of gold beads at first is repeated. Make the number of gold beads at first the same. LCM of 3 and 4 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 + 9}_{4 + 12} 
= ¹¹₁₆

(b)
Number of beads left
= 2 u + 3 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

Number of beads at first
= 16 u
= 16 x 3
= 48

Answer(s): (a) ¹¹₁₆; (b) 48