Question

u read 2/9 of my book on friday, 1/3 of it on saturday and the rest 120 pages on sunday. how many pages has my book?

Answer 1

Data:
x (pages) = ?
friday = $\frac{2}{9} x$
saturday = $\frac{1}{3} x$
the rest = 120 pages

Therefore:

$\frac{2}{9}x + \frac{1}{3}x + 120 = x$
least common multiple (9,3)
9,3 I 3
3,1 I 3
1, 1---- 3*3 = 9

Solving:
$\frac{2}{9}x + \frac{1}{3}x + 120 = x$
$\frac{2x}{\diagup\!\!\!\!9} + \frac{3x}{\diagup\!\!\!\!9} + \frac{1080}{\diagup\!\!\!\!9} = \frac{9x}{\diagup\!\!\!\!9}$
$2x + 3x + 1080 = 9x$
$2x + 3x - 9x = - 1080$
$5x - 9x = - 1080$
$- 4x = - 1080$
simplify by (-1)
$- 4x = - 1080\:*(-1)$
$4x = 1080$
$x = \frac{1080}{4}$
$\boxed{\boxed{x = 270\:pages}}\end{array}}\qquad\quad\checkmark$