PSLE
A box contained yellow and silver beads. At first, the number of yellow beads was ¹₅ the number of silver beads. After ¹₂ of the yellow beads and ⁵₈ of the silver beads were used, 152 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Yellow	Silver
Comparing yellow beads and silver beads at first	1x8 = 8 u	5x8 = 40 u
Before	2x4 = 8 u	8x5 = 40 u
Change	- 1x4 =  - 4 u	- 5x5 = - 25 u
After	1x4 =  4 u	3x5 = 15 u

(a)
The number of silver beads at first is repeated. Make the number of silver beads at first the same. LCM of 5 and 8 is 40.

The number of yellow beads at first is repeated.

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

Fraction of the beads used
= ^{4 + 25}_{8 + 40} 
= ²⁹₄₈

(b)
Number of beads left
= 4 u + 15 u
= 19 u

19 u = 152

1 u = 152 ÷ 19 = 8

Number of beads at first
= 48 u
= 48 x 8
= 384

Answer(s): (a) ²⁹₄₈; (b) 384