PSLE
A box contained silver and gold beads. At first, the number of silver beads was ¹₄ the number of gold beads. After ¹₃ of the silver beads and ⁷₉ of the gold beads were used, 112 beads were left.

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

	Silver	Gold
Comparing silver beads and gold beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 7x4 = - 28 u
After	2x3 =  6 u	2x4 = 8 u

(a)
The number of gold beads at first is repeated. Make the number of gold 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 left
= ^{6 + 8}_{9 + 36} 
= ¹⁴₄₅

(b)
Number of beads left
= 6 u + 8 u
= 14 u

14 u = 112

1 u = 112 ÷ 14 = 8

Number of beads used
= 3 u + 28 u
= 31 u
= 31 x 8
= 248

Answer(s): (a) ¹⁴₄₅; (b) 248