PSLE
A box contained silver and orange beads. At first, the number of silver beads was ¹₄ the number of orange beads. After ²₃ of the silver beads and ⁴₉ of the orange beads were used, 207 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?

	Silver	Orange
Comparing silver beads and orange beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 2x3 =  - 6 u	- 4x4 = - 16 u
After	1x3 =  3 u	5x4 = 20 u

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

The number of silver beads at first is repeated.

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

Fraction of the beads used
= ^{6 + 16}_{9 + 36} 
= ²²₄₅

(b)
Number of beads left
= 3 u + 20 u
= 23 u

23 u = 207

1 u = 207 ÷ 23 = 9

Number of beads at first
= 45 u
= 45 x 9
= 405

Answer(s): (a) ²²₄₅; (b) 405