From the total production of pencils of a factory, they sell half of their production plus 300 pencils to a company, then, they sell 1/3 of what is left minus 200 pencils to a second company and then, they sell 1/4 of what is left plus 400 pencils to a third company. If 2600 pencils remain without selling ¿How much pencils were their total production?
I made this equation:
Being "x" the total production
$$x=\frac{x}{2}+300 + \frac{x}{6}-200 + \frac{x}{12}+400 + 2600 $$
The result from this is 12400 pencils as their total production, but it doesn't seem fine, I can't see where is my mistake if you could help me I would be very thankful.
Sorry for my english, if something isn't very clear please ask.
initial: $x$
remaining after 1st customer: $x_1$
$x_1 = x - x/2 - 300$
remaining after 2nd customer: $x_2$
$x_2 = x_1 - x_1/3 + 200$
remaining after 3rd customer: $x_3$
$x_3 = x_2 - x_2/4 - 400$
And we know $x_3 = 2600$. So we just have to solve iteratively back to $x$.