PSLE
A box contained silver and green beads. At first, the number of silver beads was ¹₃ the number of green beads. After ¹₅ of the silver beads and ³₁₀ of the green beads were used, 203 beads were left.

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

	Silver	Green
Comparing silver beads and green 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 green beads at first is repeated. Make the number of green beads at first the same. 
LCM of 3 and 10 is 30.

The number of silver beads at first is repeated.

Since the number of silver beads at first is 10 u, we make the total number of silver 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 = 203

1 u = 203 ÷ 29 = 7

Number of beads used
= 2 u + 9 u
= 11 u
= 11 x 7
= 77

Answer(s): (a) ²⁹₄₀; (b) 77