PSLE
A box contained blue and gold beads. At first, the number of blue beads was ¹₄ the number of gold beads. After ¹₃ of the blue beads and ¹₉ of the gold beads were used, 266 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?

	Blue	Gold
Comparing blue beads and gold beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 1x3 =  - 3 u	- 1x4 = - 4 u
After	2x3 =  6 u	8x4 = 32 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 blue beads at first is repeated.

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

Fraction of the beads used
= ^{3 + 4}_{9 + 36} 
= ⁷₄₅

(b)
Number of beads left
= 6 u + 32 u
= 38 u

38 u = 266

1 u = 266 ÷ 38 = 7

Number of beads at first
= 45 u
= 45 x 7
= 315

Answer(s): (a) ⁷₄₅; (b) 315