PSLE
A box contained purple and green beads. At first, the number of purple beads was ¹₃ the number of green beads. After ¹₂ of the purple beads and ¹₄ of the green beads were used, 88 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	Green
Comparing purple beads and green beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	4x3 = 12 u
Change	- 1x2 =  - 2 u	- 1x3 = - 3 u
After	1x2 =  2 u	3x3 = 9 u

(a)
The number of green beads at first is repeated. Make the number of green 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 + 3}_{4 + 12} 
= ⁵₁₆

(b)
Number of beads left
= 2 u + 9 u
= 11 u

11 u = 88

1 u = 88 ÷ 11 = 8

Number of beads at first
= 16 u
= 16 x 8
= 128

Answer(s): (a) ⁵₁₆; (b) 128