PSLE
A box contained orange and red beads. At first, the number of orange beads was ¹₅ the number of red beads. After ²₃ of the orange beads and ⁷₉ of the red beads were used, 143 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	Red
Comparing orange beads and red beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 2x3 =  - 6 u	- 7x5 = - 35 u
After	1x3 =  3 u	2x5 = 10 u

(a)
The number of red beads at first is repeated. Make the number of red beads at first the same. 
LCM of 5 and 9 is 45.

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 + 10}_{9 + 45} 
= ¹³₅₄

(b)
Number of beads left
= 3 u + 10 u
= 13 u

13 u = 143

1 u = 143 ÷ 13 = 11

Number of beads used
= 6 u + 35 u
= 41 u
= 41 x 11
= 451

Answer(s): (a) ¹³₅₄; (b) 451