PSLE
A box contained green and gold beads. At first, the number of green beads was ¹₄ the number of gold beads. After ²₃ of the green beads and ⁵₉ of the gold beads were used, 209 beads were left.

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

	Green	Gold
Comparing green beads and gold beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 2x3 =  - 6 u	- 5x4 = - 20 u
After	1x3 =  3 u	4x4 = 16 u

(a)
The number of gold beads at first is repeated. Make the number of gold beads at first the same. 
LCM of 4 and 9 is 36.

The number of green beads at first is repeated.

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

Fraction of the beads left
= ^{3 + 16}_{9 + 36} 
= ¹⁹₄₅

(b)
Number of beads left
= 3 u + 16 u
= 19 u

19 u = 209

1 u = 209 ÷ 19 = 11

Number of beads used
= 6 u + 20 u
= 26 u
= 26 x 11
= 286

Answer(s): (a) ¹⁹₄₅; (b) 286