PSLE
A box contained green and black beads. At first, the number of green beads was ¹₅ the number of black beads. After ¹₄ of the green beads and ³₈ of the black beads were used, 93 beads were left.

1. What fraction of the beads were left? Leave your answer in the simplest form.
2. How many beads were used?

	Green	Black
Comparing green beads and black beads at first	1x8 = 8 u	5x8 = 40 u
Before	4x2 = 8 u	8x5 = 40 u
Change	- 1x2 =  - 2 u	- 3x5 = - 15 u
After	3x2 =  6 u	5x5 = 25 u

(a)
The number of black beads at first is repeated. Make the number of black beads at first the same. 
LCM of 5 and 8 is 40.

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 left
= ^{6 + 25}_{8 + 40} 
= ³¹₄₈

(b)
Number of beads left
= 6 u + 25 u
= 31 u

31 u = 93

1 u = 93 ÷ 31 = 3

Number of beads used
= 2 u + 15 u
= 17 u
= 17 x 3
= 51

Answer(s): (a) ³¹₄₈; (b) 51