Sin Ling had 360 blue, green and white beads at first. After using $\tfrac{1}{4}$ of the blue beads, $\tfrac{2}{3}$ of the green beads and $\tfrac{8}{9}$ of the white beads, she had an equal number of each coloured beads left. Find the number of blue beads left.

1. Find the fraction of beads left for each colour.

Fraction of blue beads left = $1 - \frac{1}{4} = \frac{3}{4}$
Fraction of green beads left = $1 - \frac{2}{3} = \frac{1}{3}$
Fraction of white beads left = $1 - \frac{8}{9} = \frac{1}{9}$

2. Make the numerators of the fractions equal to represent the equal number of beads left.

Since the number of beads left for each colour is equal, we make the numerators the same (LCM of 3, 1, and 1 is 3):
$\frac{3}{4}$ of blue beads = $\frac{3}{9}$ of green beads = $\frac{3}{27}$ of white beads

This means the number of beads left for each colour is $3$ units.

3. Find the total number of units at first and the value of 1 unit.

Total units at first = $4 + 9 + 27 = 40$ units
$40$ units = $360$
$1$ unit = $360 \div 40 = 9$

4. Calculate the number of blue beads left.

Number of blue beads left = $3$ units
$3 \times 9 = 27$