PSLE
A box contained silver and orange beads. At first, the number of silver beads was ¹₃ the number of orange beads. After ²₅ of the silver beads and ³₁₀ of the orange beads were used, 216 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	Orange
Comparing silver beads and orange beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 2x2 =  - 4 u	- 3x3 = - 9 u
After	3x2 =  6 u	7x3 = 21 u

(a)
The number of orange beads at first is repeated. Make the number of orange beads at first the same. 
LCM of 3 and 10 is 30.

The number of silver beads at first is repeated.

Since the number of silver beads at first is 10 u, we make the total number of silver beads at first the same by multiplying 5 by 2 to become 10 u too.

Fraction of the beads left
= ^{6 + 21}_{10 + 30} 
= ²⁷₄₀

(b)
Number of beads left
= 6 u + 21 u
= 27 u

27 u = 216

1 u = 216 ÷ 27 = 8

Number of beads used
= 4 u + 9 u
= 13 u
= 13 x 8
= 104

Answer(s): (a) ²⁷₄₀; (b) 104