PSLE
A box contained red and black beads. At first, the number of red beads was ¹₃ the number of black beads. After ¹₅ of the red beads and ³₁₀ of the black beads were used, 261 beads were left.

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

	Red	Black
Comparing red beads and black beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 1x2 =  - 2 u	- 3x3 = - 9 u
After	4x2 =  8 u	7x3 = 21 u

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

The number of red beads at first is repeated.

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

Fraction of the beads left
= ^{8 + 21}_{10 + 30} 
= ²⁹₄₀

(b)
Number of beads left
= 8 u + 21 u
= 29 u

29 u = 261

1 u = 261 ÷ 29 = 9

Number of beads used
= 2 u + 9 u
= 11 u
= 11 x 9
= 99

Answer(s): (a) ²⁹₄₀; (b) 99