PSLE
A box contained purple and yellow beads. At first, the number of purple beads was ¹₃ the number of yellow beads. After ³₅ of the purple beads and ⁹₁₀ of the yellow beads were used, 63 beads were left.

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

	Purple	Yellow
Comparing purple beads and yellow beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 3x2 =  - 6 u	- 9x3 = - 27 u
After	2x2 =  4 u	1x3 = 3 u

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

The number of purple beads at first is repeated.

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

Fraction of the beads left
= ^{4 + 3}_{10 + 30} 
= ⁷₄₀

(b)
Number of beads left
= 4 u + 3 u
= 7 u

7 u = 63

1 u = 63 ÷ 7 = 9

Number of beads used
= 6 u + 27 u
= 33 u
= 33 x 9
= 297

Answer(s): (a) ⁷₄₀; (b) 297