PSLE
A box contained blue and purple beads. At first, the number of blue beads was ¹₄ the number of purple beads. After ²₃ of the blue beads and ⁷₉ of the purple beads were used, 99 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	Purple
Comparing blue beads and purple beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 2x3 =  - 6 u	- 7x4 = - 28 u
After	1x3 =  3 u	2x4 = 8 u

(a)
The number of purple beads at first is repeated. Make the number of purple 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
= ^{6 + 28}_{9 + 36} 
= ³⁴₄₅

(b)
Number of beads left
= 3 u + 8 u
= 11 u

11 u = 99

1 u = 99 ÷ 11 = 9

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

Answer(s): (a) ³⁴₄₅; (b) 405