PSLE
A box contained silver and blue beads. At first, the number of silver beads was ¹₅ the number of blue beads. After ¹₄ of the silver beads and ⁷₈ of the blue beads were used, 55 beads were left.

1. What fraction of the beads were left? Leave your answer in the simplest form.
2. How many beads were used?

	Silver	Blue
Comparing silver beads and blue beads at first	1x8 = 8 u	5x8 = 40 u
Before	4x2 = 8 u	8x5 = 40 u
Change	- 1x2 =  - 2 u	- 7x5 = - 35 u
After	3x2 =  6 u	1x5 = 5 u

(a)
The number of blue beads at first is repeated. Make the number of blue beads at first the same. 
LCM of 5 and 8 is 40.

The number of silver beads at first is repeated.

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

Fraction of the beads left
= ^{6 + 5}_{8 + 40} 
= ¹¹₄₈

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

11 u = 55

1 u = 55 ÷ 11 = 5

Number of beads used
= 2 u + 35 u
= 37 u
= 37 x 5
= 185

Answer(s): (a) ¹¹₄₈; (b) 185