PSLE
A box contained yellow and silver beads. At first, the number of yellow beads was ¹₅ the number of silver beads. After ²₃ of the yellow beads and ⁵₉ of the silver beads were used, 230 beads were left.

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

	Yellow	Silver
Comparing yellow beads and silver beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 2x3 =  - 6 u	- 5x5 = - 25 u
After	1x3 =  3 u	4x5 = 20 u

(a)
The number of silver beads at first is repeated. Make the number of silver beads at first the same. 
LCM of 5 and 9 is 45.

The number of yellow beads at first is repeated.

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

Fraction of the beads left
= ^{3 + 20}_{9 + 45} 
= ²³₅₄

(b)
Number of beads left
= 3 u + 20 u
= 23 u

23 u = 230

1 u = 230 ÷ 23 = 10

Number of beads used
= 6 u + 25 u
= 31 u
= 31 x 10
= 310

Answer(s): (a) ²³₅₄; (b) 310