PSLE
A box contained pink and gold beads. At first, the number of pink beads was ¹₃ the number of gold beads. After ³₅ of the pink beads and ⁷₁₀ of the gold beads were used, 104 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	Gold
Comparing pink beads and gold beads at first	1x10 = 10 u	3x10 = 30 u
Before	5x2 = 10 u	10x3 = 30 u
Change	- 3x2 =  - 6 u	- 7x3 = - 21 u
After	2x2 =  4 u	3x3 = 9 u

(a)
The number of gold beads at first is repeated. Make the number of gold 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 left
= ^{4 + 9}_{10 + 30} 
= ¹³₄₀

(b)
Number of beads left
= 4 u + 9 u
= 13 u

13 u = 104

1 u = 104 ÷ 13 = 8

Number of beads used
= 6 u + 21 u
= 27 u
= 27 x 8
= 216

Answer(s): (a) ¹³₄₀; (b) 216