PSLE
A box contained green and yellow beads. At first, the number of green beads was ¹₅ the number of yellow beads. After ¹₂ of the green beads and ³₄ of the yellow beads were used, 42 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?

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

The number of green beads at first is repeated.

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

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

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

7 u = 42

1 u = 42 ÷ 7 = 6

Number of beads at first
= 24 u
= 24 x 6
= 144

Answer(s): (a) ¹⁷₂₄; (b) 144