PSLE
A box contained gold and green beads. At first, the number of gold beads was ¹₃ the number of green beads. After ²₅ of the gold beads and ⁹₁₀ of the green beads were used, 45 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Gold	Green
Comparing gold beads and green beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 2x2 =  - 4 u	- 9x3 = - 27 u
After	3x2 =  6 u	1x3 = 3 u

(a)
The number of green beads at first is repeated. Make the number of green beads at first the same. LCM of 3 and 10 is 30.

The number of gold beads at first is repeated.

Since the number of gold beads at first is 10 u, we make the total number of gold beads at first the same by multiplying 5 by 2 to become 10 u too.

Fraction of the beads used
= ^{4 + 27}_{10 + 30} 
= ³¹₄₀

(b)
Number of beads left
= 6 u + 3 u
= 9 u

9 u = 45

1 u = 45 ÷ 9 = 5

Number of beads at first
= 40 u
= 40 x 5
= 200

Answer(s): (a) ³¹₄₀; (b) 200