PSLE
A box contained yellow and black beads. At first, the number of yellow beads was ¹₄ the number of black beads. After ¹₃ of the yellow beads and ²₉ of the black beads were used, 204 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?

	Yellow	Black
Comparing yellow beads and black beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 2x4 = - 8 u
After	2x3 =  6 u	7x4 = 28 u

(a)
The number of black beads at first is repeated. Make the number of black beads at first the same. LCM of 4 and 9 is 36.

The number of yellow beads at first is repeated.

Since the number of yellow beads at first is 9 u, we make the total number of yellow beads at first the same by multiplying 3 by 3 to become 9 u too.

Fraction of the beads used
= ^{3 + 8}_{9 + 36} 
= ¹¹₄₅

(b)
Number of beads left
= 6 u + 28 u
= 34 u

34 u = 204

1 u = 204 ÷ 34 = 6

Number of beads at first
= 45 u
= 45 x 6
= 270

Answer(s): (a) ¹¹₄₅; (b) 270