PSLE
A box contained blue and orange beads. At first, the number of blue beads was ¹₄ the number of orange beads. After ¹₃ of the blue beads and ²₉ of the orange beads were used, 102 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?

	Blue	Orange
Comparing blue beads and orange 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 orange beads at first is repeated. Make the number of orange beads at first the same. LCM of 4 and 9 is 36.

The number of blue beads at first is repeated.

Since the number of blue beads at first is 9 u, we make the total number of blue 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 = 102

1 u = 102 ÷ 34 = 3

Number of beads at first
= 45 u
= 45 x 3
= 135

Answer(s): (a) ¹¹₄₅; (b) 135