PSLE
A box contained black and green beads. At first, the number of black beads was ¹₃ the number of green beads. After ¹₄ of the black beads and ⁷₈ of the green beads were used, 90 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	Green
Comparing black beads and green beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 1x2 =  - 2 u	- 7x3 = - 21 u
After	3x2 =  6 u	1x3 = 3 u

(a)
The number of green beads at first is repeated. Make the number of green beads at first the same. LCM of 3 and 8 is 24.

The number of black beads at first is repeated.

Since the number of black beads at first is 8 u, we make the total number of black beads at first the same by multiplying 4 by 2 to become 8 u too.

Fraction of the beads used
= ^{2 + 21}_{8 + 24} 
= ²³₃₂

(b)
Number of beads left
= 6 u + 3 u
= 9 u

9 u = 90

1 u = 90 ÷ 9 = 10

Number of beads at first
= 32 u
= 32 x 10
= 320

Answer(s): (a) ²³₃₂; (b) 320