PSLE
A box contained gold and orange beads. At first, the number of gold beads was ¹₅ the number of orange beads. After ¹₃ of the gold beads and ²₉ of the orange beads were used, 451 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	Orange
Comparing gold beads and orange beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 1x3 =  - 3 u	- 2x5 = - 10 u
After	2x3 =  6 u	7x5 = 35 u

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

The number of gold beads at first is repeated.

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

Fraction of the beads left
= ^{6 + 35}_{9 + 45} 
= ⁴¹₅₄

(b)
Number of beads left
= 6 u + 35 u
= 41 u

41 u = 451

1 u = 451 ÷ 41 = 11

Number of beads used
= 3 u + 10 u
= 13 u
= 13 x 11
= 143

Answer(s): (a) ⁴¹₅₄; (b) 143