PSLE
A box contained black and yellow beads. At first, the number of black beads was ¹₃ the number of yellow beads. After ³₅ of the black beads and ¹₁₀ of the yellow beads were used, 310 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?

	Black	Yellow
Comparing black beads and yellow 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 yellow beads at first is repeated. Make the number of yellow beads at first the same. LCM of 3 and 10 is 30.

The number of black beads at first is repeated.

Since the number of black beads at first is 10 u, we make the total number of black 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 = 310

1 u = 310 ÷ 31 = 10

Number of beads at first
= 40 u
= 40 x 10
= 400

Answer(s): (a) ⁹₄₀; (b) 400