PSLE
A box contained gold and purple beads. At first, the number of gold beads was ¹₅ the number of purple beads. After ¹₂ of the gold beads and ¹₄ of the purple beads were used, 204 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?

	Gold	Purple
Comparing gold beads and purple beads at first	1x4 = 4 u	5x4 = 20 u
Before	2x2 = 4 u	4x5 = 20 u
Change	- 1x2 =  - 2 u	- 1x5 = - 5 u
After	1x2 =  2 u	3x5 = 15 u

(a)
The number of purple beads at first is repeated. Make the number of purple beads at first the same. LCM of 5 and 4 is 20.

The number of gold beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 5}_{4 + 20} 
= ⁷₂₄

(b)
Number of beads left
= 2 u + 15 u
= 17 u

17 u = 204

1 u = 204 ÷ 17 = 12

Number of beads at first
= 24 u
= 24 x 12
= 288

Answer(s): (a) ⁷₂₄; (b) 288