PSLE
A box contained gold and yellow beads. At first, the number of gold beads was ¹₅ the number of yellow beads. After ¹₄ of the gold beads and ³₈ of the yellow beads were used, 186 beads were left.

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

	Gold	Yellow
Comparing gold beads and yellow beads at first	1x8 = 8 u	5x8 = 40 u
Before	4x2 = 8 u	8x5 = 40 u
Change	- 1x2 =  - 2 u	- 3x5 = - 15 u
After	3x2 =  6 u	5x5 = 25 u

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

The number of gold beads at first is repeated.

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

Fraction of the beads left
= ^{6 + 25}_{8 + 40} 
= ³¹₄₈

(b)
Number of beads left
= 6 u + 25 u
= 31 u

31 u = 186

1 u = 186 ÷ 31 = 6

Number of beads used
= 2 u + 15 u
= 17 u
= 17 x 6
= 102

Answer(s): (a) ³¹₄₈; (b) 102