PSLE
A box contained silver and purple beads. At first, the number of silver beads was ¹₃ the number of purple beads. After ¹₅ of the silver beads and ⁷₁₀ of the purple beads were used, 51 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?

	Silver	Purple
Comparing silver beads and purple beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 1x2 =  - 2 u	- 7x3 = - 21 u
After	4x2 =  8 u	3x3 = 9 u

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

The number of silver beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 21}_{10 + 30} 
= ²³₄₀

(b)
Number of beads left
= 8 u + 9 u
= 17 u

17 u = 51

1 u = 51 ÷ 17 = 3

Number of beads at first
= 40 u
= 40 x 3
= 120

Answer(s): (a) ²³₄₀; (b) 120