PSLE
A box contained black and blue beads. At first, the number of black beads was ¹₄ the number of blue beads. After ¹₃ of the black beads and ²₉ of the blue beads were used, 272 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?

	Black	Blue
Comparing black beads and blue beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 2x4 = - 8 u
After	2x3 =  6 u	7x4 = 28 u

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

The number of black beads at first is repeated.

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

Fraction of the beads used
= ^{3 + 8}_{9 + 36} 
= ¹¹₄₅

(b)
Number of beads left
= 6 u + 28 u
= 34 u

34 u = 272

1 u = 272 ÷ 34 = 8

Number of beads at first
= 45 u
= 45 x 8
= 360

Answer(s): (a) ¹¹₄₅; (b) 360