Mark has 312 books in his bookcases. he has 11 times as many fiction books as nonfiction books. how many fiction books does mark have?

With the information given we can wirte down 2 different equations where:
x = How many Fictoon books there are
A nd y = How many non-fiction books there are :
#1) x + y = 312
( The total of the books is 312 )

#2) x = 11y
(He has 11 times as many firction books as he has non-ficton books)

Now what we need to do is to isolate one the variables ( x or y ) , get its value and apply to one the equations to get the other variable's value:
We can do that by the property of substitution:

If x = 11y
then x + y = (11y) + y = 12y

If x + y = 312
and x + y = 12y
then 12y = 312

Now with the equation 12y = 312 , we can isolate y by dividing both sides of the equation by 12 :
12/12y = 312/12
y = 26
What that means : Mark has 26 non-fictional books.

Now that we have the value of y , we can find the value of x by plugging y to one of the equations :

x + y = 312
or
x = 7y
( I will do both , but you dont need to )

x + y = 312
Plugin 26 for y :
x + 26 = 312

Shift 26 to the other side of the equation by subtracting both sides of the equation by 26:
x + 26 - 26 = 312 - 26
26 - 26 cancel out , so we end up with :
x = 286

Second Equation :
x = 11y
Plugin 26 for y:
x = 11 × 26

x = 286

Awnser : Mark has 286 fictoon books and 26 non-fiction !

I hope you understood my brief explanation. And please consider marking this awnser as Branliest. Thank you ! :)