PSLE
A box contained pink and orange beads. At first, the number of pink beads was ¹₃ the number of orange beads. After ¹₂ of the pink beads and ¹₄ of the orange 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?

	Pink	Orange
Comparing pink beads and orange 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 orange beads at first is repeated. Make the number of orange beads at first the same. LCM of 3 and 4 is 12.

The number of pink beads at first is repeated.

Since the number of pink beads at first is 4 u, we make the total number of pink 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