PSLE
A box contained silver and red beads. At first, the number of silver beads was ¹₅ the number of red beads. After ¹₃ of the silver beads and ¹₆ of the red beads were used, 174 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	Red
Comparing silver beads and red beads at first	1x6 = 6 u	5x6 = 30 u
Before	3x2 = 6 u	6x5 = 30 u
Change	- 1x2 =  - 2 u	- 1x5 = - 5 u
After	2x2 =  4 u	5x5 = 25 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 6 is 30.

The number of silver beads at first is repeated.

Since the number of silver beads at first is 6 u, we make the total number of silver beads at first the same by multiplying 3 by 2 to become 6 u too.

Fraction of the beads used
= ^{2 + 5}_{6 + 30} 
= ⁷₃₆

(b)
Number of beads left
= 4 u + 25 u
= 29 u

29 u = 174

1 u = 174 ÷ 29 = 6

Number of beads at first
= 36 u
= 36 x 6
= 216

Answer(s): (a) ⁷₃₆; (b) 216