PSLE
A box contained purple and black beads. At first, the number of purple beads was ¹₄ the number of black beads. After ²₃ of the purple beads and ⁷₉ of the black beads were used, 66 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?

	Purple	Black
Comparing purple beads and black 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 black beads at first is repeated. Make the number of black beads at first the same. LCM of 4 and 9 is 36.

The number of purple beads at first is repeated.

Since the number of purple beads at first is 9 u, we make the total number of purple 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 = 66

1 u = 66 ÷ 11 = 6

Number of beads at first
= 45 u
= 45 x 6
= 270

Answer(s): (a) ³⁴₄₅; (b) 270