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 ¹₄ of the purple beads were used, 136 beads were left.

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

	Black	Purple
Comparing black beads and purple beads at first	1x4 = 4 u	5x4 = 20 u
Before	2x2 = 4 u	4x5 = 20 u
Change	- 1x2 =  - 2 u	- 1x5 = - 5 u
After	1x2 =  2 u	3x5 = 15 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 4 is 20.

The number of black beads at first is repeated.

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

Fraction of the beads left
= ^{2 + 15}_{4 + 20} 
= ¹⁷₂₄

(b)
Number of beads left
= 2 u + 15 u
= 17 u

17 u = 136

1 u = 136 ÷ 17 = 8

Number of beads used
= 2 u + 5 u
= 7 u
= 7 x 8
= 56

Answer(s): (a) ¹⁷₂₄; (b) 56