PSLE
A box contained purple and gold beads. At first, the number of purple beads was ¹₃ the number of gold beads. After ¹₅ of the purple beads and ³₁₀ of the gold beads were used, 174 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	Gold
Comparing purple beads and gold beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 1x2 =  - 2 u	- 3x3 = - 9 u
After	4x2 =  8 u	7x3 = 21 u

(a)
The number of gold beads at first is repeated. Make the number of gold beads at first the same. LCM of 3 and 10 is 30.

The number of purple beads at first is repeated.

Since the number of purple beads at first is 10 u, we make the total number of purple beads at first the same by multiplying 5 by 2 to become 10 u too.

Fraction of the beads used
= ^{2 + 9}_{10 + 30} 
= ¹¹₄₀

(b)
Number of beads left
= 8 u + 21 u
= 29 u

29 u = 174

1 u = 174 ÷ 29 = 6

Number of beads at first
= 40 u
= 40 x 6
= 240

Answer(s): (a) ¹¹₄₀; (b) 240