PSLE
A box contained orange and green beads. At first, the number of orange beads was ¹₅ the number of green beads. After ¹₂ of the orange beads and ¹₄ of the green beads were used, 204 beads were left.

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

	Orange	Green
Comparing orange beads and green 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 green beads at first is repeated. Make the number of green beads at first the same. 
LCM of 5 and 4 is 20.

The number of orange beads at first is repeated.

Since the number of orange beads at first is 4 u, we make the total number of orange 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 = 204

1 u = 204 ÷ 17 = 12

Number of beads used
= 2 u + 5 u
= 7 u
= 7 x 12
= 84

Answer(s): (a) ¹⁷₂₄; (b) 84