PSLE
A box contained blue and purple beads. At first, the number of blue beads was ¹₃ the number of purple beads. After ³₅ of the blue beads and ⁷₁₀ of the purple beads were used, 117 beads were left.

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

	Blue	Purple
Comparing blue beads and purple beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 3x2 =  - 6 u	- 7x3 = - 21 u
After	2x2 =  4 u	3x3 = 9 u

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

The number of blue beads at first is repeated.

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

Fraction of the beads left
= ^{4 + 9}_{10 + 30} 
= ¹³₄₀

(b)
Number of beads left
= 4 u + 9 u
= 13 u

13 u = 117

1 u = 117 ÷ 13 = 9

Number of beads used
= 6 u + 21 u
= 27 u
= 27 x 9
= 243

Answer(s): (a) ¹³₄₀; (b) 243