PSLE
A box contained green and purple beads. At first, the number of green beads was ¹₅ the number of purple beads. After ¹₄ of the green beads and ⁷₈ of the purple beads were used, 88 beads were left.

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

	Green	Purple
Comparing green beads and purple beads at first	1x8 = 8 u	5x8 = 40 u
Before	4x2 = 8 u	8x5 = 40 u
Change	- 1x2 =  - 2 u	- 7x5 = - 35 u
After	3x2 =  6 u	1x5 = 5 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 green beads at first is repeated.

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

Fraction of the beads left
= ^{6 + 5}_{8 + 40} 
= ¹¹₄₈

(b)
Number of beads left
= 6 u + 5 u
= 11 u

11 u = 88

1 u = 88 ÷ 11 = 8

Number of beads used
= 2 u + 35 u
= 37 u
= 37 x 8
= 296

Answer(s): (a) ¹¹₄₈; (b) 296