PSLE
A box contained pink and red beads. At first, the number of pink beads was ¹₃ the number of red beads. After ³₅ of the pink beads and ⁹₁₀ of the red beads were used, 77 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?

	Pink	Red
Comparing pink beads and red 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 red beads at first is repeated. Make the number of red beads at first the same. LCM of 3 and 10 is 30.

The number of pink beads at first is repeated.

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

Fraction of the beads used
= ^{6 + 27}_{10 + 30} 
= ³³₄₀

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

7 u = 77

1 u = 77 ÷ 7 = 11

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

Answer(s): (a) ³³₄₀; (b) 440