PSLE
A box contained red and green beads. At first, the number of red beads was ¹₃ the number of green beads. After ³₄ of the red beads and ¹₈ of the green beads were used, 138 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?

	Red	Green
Comparing red beads and green beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 3x2 =  - 6 u	- 1x3 = - 3 u
After	1x2 =  2 u	7x3 = 21 u

(a)
The number of green beads at first is repeated. Make the number of green beads at first the same. LCM of 3 and 8 is 24.

The number of red beads at first is repeated.

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

Fraction of the beads used
= ^{6 + 3}_{8 + 24} 
= ⁹₃₂

(b)
Number of beads left
= 2 u + 21 u
= 23 u

23 u = 138

1 u = 138 ÷ 23 = 6

Number of beads at first
= 32 u
= 32 x 6
= 192

Answer(s): (a) ⁹₃₂; (b) 192