PSLE
A box contained purple and red beads. At first, the number of purple beads was ¹₃ the number of red beads. After ¹₄ of the purple beads and ⁷₈ of the red beads were used, 27 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	Red
Comparing purple beads and red beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 1x2 =  - 2 u	- 7x3 = - 21 u
After	3x2 =  6 u	1x3 = 3 u

(a)
The number of red beads at first is repeated. Make the number of red beads at first the same. LCM of 3 and 8 is 24.

The number of purple beads at first is repeated.

Since the number of purple beads at first is 8 u, we make the total number of purple beads at first the same by multiplying 4 by 2 to become 8 u too.

Fraction of the beads used
= ^{2 + 21}_{8 + 24} 
= ²³₃₂

(b)
Number of beads left
= 6 u + 3 u
= 9 u

9 u = 27

1 u = 27 ÷ 9 = 3

Number of beads at first
= 32 u
= 32 x 3
= 96

Answer(s): (a) ²³₃₂; (b) 96