PSLE
A box contained pink and silver beads. At first, the number of pink beads was ¹₃ the number of silver beads. After ¹₂ of the pink beads and ⁷₈ of the silver beads were used, 42 beads were left.

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

	Pink	Silver
Comparing pink beads and silver beads at first	1x8 = 8 u	3x8 = 24 u
Before	2x4 = 8 u	8x3 = 24 u
Change	- 1x4 =  - 4 u	- 7x3 = - 21 u
After	1x4 =  4 u	1x3 = 3 u

(a)
The number of silver beads at first is repeated. Make the number of silver beads at first the same. 
LCM of 3 and 8 is 24.

The number of pink beads at first is repeated.

Since the number of pink beads at first is 8 u, we make the total number of pink beads at first the same by multiplying 2 by 4 to become 8 u too.

Fraction of the beads left
= ^{4 + 3}_{8 + 24} 
= ⁷₃₂

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

7 u = 42

1 u = 42 ÷ 7 = 6

Number of beads used
= 4 u + 21 u
= 25 u
= 25 x 6
= 150

Answer(s): (a) ⁷₃₂; (b) 150