PSLE
A box contained pink and purple beads. At first, the number of pink beads was ¹₄ the number of purple beads. After ¹₃ of the pink beads and ²₉ of the purple beads were used, 340 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?

	Pink	Purple
Comparing pink beads and purple 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 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 pink beads at first is repeated.

Since the number of pink beads at first is 9 u, we make the total number of pink 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 = 340

1 u = 340 ÷ 34 = 10

Number of beads at first
= 45 u
= 45 x 10
= 450

Answer(s): (a) ¹¹₄₅; (b) 450