PSLE
A box contained blue and red beads. At first, the number of blue beads was ¹₅ the number of red beads. After ¹₂ of the blue beads and ¹₄ of the red beads were used, 187 beads were left.

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

	Blue	Red
Comparing blue beads and red beads at first	1x4 = 4 u	5x4 = 20 u
Before	2x2 = 4 u	4x5 = 20 u
Change	- 1x2 =  - 2 u	- 1x5 = - 5 u
After	1x2 =  2 u	3x5 = 15 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 4 is 20.

The number of blue beads at first is repeated.

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

Fraction of the beads left
= ^{2 + 15}_{4 + 20} 
= ¹⁷₂₄

(b)
Number of beads left
= 2 u + 15 u
= 17 u

17 u = 187

1 u = 187 ÷ 17 = 11

Number of beads used
= 2 u + 5 u
= 7 u
= 7 x 11
= 77

Answer(s): (a) ¹⁷₂₄; (b) 77