PSLE
A box contained green and purple beads. At first, the number of green beads was ¹₃ the number of purple beads. After ³₄ of the green beads and ⁵₈ of the purple 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?

	Green	Purple
Comparing green beads and purple beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 3x2 =  - 6 u	- 5x3 = - 15 u
After	1x2 =  2 u	3x3 = 9 u

(a)
The number of purple beads at first is repeated. Make the number of purple beads at first the same. LCM of 3 and 8 is 24.

The number of green beads at first is repeated.

Since the number of green beads at first is 8 u, we make the total number of green beads at first the same by multiplying 4 by 2 to become 8 u too.

Fraction of the beads used
= ^{6 + 15}_{8 + 24} 
= ²¹₃₂

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

11 u = 88

1 u = 88 ÷ 11 = 8

Number of beads at first
= 32 u
= 32 x 8
= 256

Answer(s): (a) ²¹₃₂; (b) 256