PSLE
A box contained green and red beads. At first, the number of green beads was ¹₄ the number of red beads. After ¹₃ of the green beads and ¹₉ of the red beads were used, 342 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	Red
Comparing green beads and red beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 1x4 = - 4 u
After	2x3 =  6 u	8x4 = 32 u

(a)
The number of red beads at first is repeated. Make the number of red beads at first the same. LCM of 4 and 9 is 36.

The number of green beads at first is repeated.

Since the number of green beads at first is 9 u, we make the total number of green beads at first the same by multiplying 3 by 3 to become 9 u too.

Fraction of the beads used
= ^{3 + 4}_{9 + 36} 
= ⁷₄₅

(b)
Number of beads left
= 6 u + 32 u
= 38 u

38 u = 342

1 u = 342 ÷ 38 = 9

Number of beads at first
= 45 u
= 45 x 9
= 405

Answer(s): (a) ⁷₄₅; (b) 405