PSLE
A box contained yellow and green beads. At first, the number of yellow beads was ¹₄ the number of green beads. After ²₃ of the yellow beads and ²₉ of the green beads were used, 279 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?

	Yellow	Green
Comparing yellow beads and green beads at first	1x9 = 9 u	4x9 = 36 u
Before	3x3 = 9 u	9x4 = 36 u
Change	- 2x3 =  - 6 u	- 2x4 = - 8 u
After	1x3 =  3 u	7x4 = 28 u

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

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 used
= ^{6 + 8}_{9 + 36} 
= ¹⁴₄₅

(b)
Number of beads left
= 3 u + 28 u
= 31 u

31 u = 279

1 u = 279 ÷ 31 = 9

Number of beads at first
= 45 u
= 45 x 9
= 405

Answer(s): (a) ¹⁴₄₅; (b) 405