PSLE
A box contained red and yellow beads. At first, the number of red beads was ¹₃ the number of yellow beads. After ¹₅ of the red beads and ³₁₀ of the yellow beads were used, 319 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?

	Red	Yellow
Comparing red beads and yellow 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 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 red beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 9}_{10 + 30} 
= ¹¹₄₀

(b)
Number of beads left
= 8 u + 21 u
= 29 u

29 u = 319

1 u = 319 ÷ 29 = 11

Number of beads at first
= 40 u
= 40 x 11
= 440

Answer(s): (a) ¹¹₄₀; (b) 440