PSLE
A box contained black and purple beads. At first, the number of black beads was ¹₅ the number of purple beads. After ¹₂ of the black beads and ³₈ 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?

	Black	Purple
Comparing black beads and purple beads at first	1x8 = 8 u	5x8 = 40 u
Before	2x4 = 8 u	8x5 = 40 u
Change	- 1x4 =  - 4 u	- 3x5 = - 15 u
After	1x4 =  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 8 is 40.

The number of black beads at first is repeated.

Since the number of black beads at first is 8 u, we make the total number of black beads at first the same by multiplying 2 by 4 to become 8 u too.

Fraction of the beads used
= ^{4 + 15}_{8 + 40} 
= ¹⁹₄₈

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

29 u = 319

1 u = 319 ÷ 29 = 11

Number of beads at first
= 48 u
= 48 x 11
= 528

Answer(s): (a) ¹⁹₄₈; (b) 528