PSLE
A box contained green and silver beads. At first, the number of green beads was ¹₃ the number of silver beads. After ¹₄ of the green beads and ⁵₈ of the silver beads were used, 60 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	Silver
Comparing green beads and silver beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 1x2 =  - 2 u	- 5x3 = - 15 u
After	3x2 =  6 u	3x3 = 9 u

(a)
The number of silver beads at first is repeated. Make the number of silver 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
= ^{2 + 15}_{8 + 24} 
= ¹⁷₃₂

(b)
Number of beads left
= 6 u + 9 u
= 15 u

15 u = 60

1 u = 60 ÷ 15 = 4

Number of beads at first
= 32 u
= 32 x 4
= 128

Answer(s): (a) ¹⁷₃₂; (b) 128