PSLE
A box contained orange and black beads. At first, the number of orange beads was ¹₄ the number of black beads. After ²₃ of the orange beads and ²₉ of the black beads were used, 279 beads were left.

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

	Orange	Black
Comparing orange beads and black beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 2x3 =  - 6 u	- 2x4 = - 8 u
After	1x3 =  3 u	7x4 = 28 u

(a)
The number of black beads at first is repeated. Make the number of black beads at first the same. 
LCM of 4 and 9 is 36.

The number of orange beads at first is repeated.

Since the number of orange beads at first is 9 u, we make the total number of orange beads at first the same by multiplying 3 by 3 to become 9 u too.

Fraction of the beads left
= ^{3 + 28}_{9 + 36} 
= ³¹₄₅

(b)
Number of beads left
= 3 u + 28 u
= 31 u

31 u = 279

1 u = 279 ÷ 31 = 9

Number of beads used
= 6 u + 8 u
= 14 u
= 14 x 9
= 126

Answer(s): (a) ³¹₄₅; (b) 126