PSLE
A box contained orange and black beads. At first, the number of orange beads was ¹₃ the number of black beads. After ³₅ of the orange beads and ¹₁₀ of the black beads were used, 124 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?

	Orange	Black
Comparing orange beads and black beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 3x2 =  - 6 u	- 1x3 = - 3 u
After	2x2 =  4 u	9x3 = 27 u

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

The number of orange beads at first is repeated.

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

Fraction of the beads used
= ^{6 + 3}_{10 + 30} 
= ⁹₄₀

(b)
Number of beads left
= 4 u + 27 u
= 31 u

31 u = 124

1 u = 124 ÷ 31 = 4

Number of beads at first
= 40 u
= 40 x 4
= 160

Answer(s): (a) ⁹₄₀; (b) 160