PSLE
A box contained orange and red beads. At first, the number of orange beads was ¹₅ the number of red beads. After ¹₂ of the orange beads and ³₄ of the red beads were used, 35 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	Red
Comparing orange beads and red beads at first	1x4 = 4 u	5x4 = 20 u
Before	2x2 = 4 u	4x5 = 20 u
Change	- 1x2 =  - 2 u	- 3x5 = - 15 u
After	1x2 =  2 u	1x5 = 5 u

(a)
The number of red beads at first is repeated. Make the number of red 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 + 5}_{4 + 20} 
= ⁷₂₄

(b)
Number of beads left
= 2 u + 5 u
= 7 u

7 u = 35

1 u = 35 ÷ 7 = 5

Number of beads used
= 2 u + 15 u
= 17 u
= 17 x 5
= 85

Answer(s): (a) ⁷₂₄; (b) 85