PSLE
A box contained blue and red beads. At first, the number of blue beads was ¹₅ the number of red beads. After ¹₃ of the blue beads and ⁸₉ of the red beads were used, 55 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?

	Blue	Red
Comparing blue beads and red beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 1x3 =  - 3 u	- 8x5 = - 40 u
After	2x3 =  6 u	1x5 = 5 u

(a)
The number of red beads at first is repeated. Make the number of red beads at first the same. LCM of 5 and 9 is 45.

The number of blue beads at first is repeated.

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

Fraction of the beads used
= ^{3 + 40}_{9 + 45} 
= ⁴³₅₄

(b)
Number of beads left
= 6 u + 5 u
= 11 u

11 u = 55

1 u = 55 ÷ 11 = 5

Number of beads at first
= 54 u
= 54 x 5
= 270

Answer(s): (a) ⁴³₅₄; (b) 270