PSLE
A box contained gold and green beads. At first, the number of gold beads was ¹₅ the number of green beads. After ¹₂ of the gold beads and ³₈ of the green beads were used, 261 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	Green
Comparing gold beads and green beads at first	1x8 = 8 u	5x8 = 40 u
Before	2x4 = 8 u	8x5 = 40 u
Change	- 1x4 =  - 4 u	- 3x5 = - 15 u
After	1x4 =  4 u	5x5 = 25 u

(a)
The number of green beads at first is repeated. Make the number of green 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 2 by 4 to become 8 u too.

Fraction of the beads left
= ^{4 + 25}_{8 + 40} 
= ²⁹₄₈

(b)
Number of beads left
= 4 u + 25 u
= 29 u

29 u = 261

1 u = 261 ÷ 29 = 9

Number of beads used
= 4 u + 15 u
= 19 u
= 19 x 9
= 171

Answer(s): (a) ²⁹₄₈; (b) 171