PSLE
A box contained red and purple beads. At first, the number of red beads was ¹₅ the number of purple beads. After ¹₃ of the red beads and ¹₆ of the purple beads were used, 319 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?

	Red	Purple
Comparing red beads and purple 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 purple beads at first is repeated. Make the number of purple beads at first the same. LCM of 5 and 6 is 30.

The number of red beads at first is repeated.

Since the number of red beads at first is 6 u, we make the total number of red 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 = 319

1 u = 319 ÷ 29 = 11

Number of beads at first
= 36 u
= 36 x 11
= 396

Answer(s): (a) ⁷₃₆; (b) 396