Answer:
Let's call x as the number of friends, now, in Theatre A we have:
Price for x tickets = x*$14.50
price for 3 tubs of popcorn = 3*$5.75 = $17.25
Total price:
Pa(x) = $14.50*x + $17.25
Now, for Theatre B we have:
Price for x tickets = $13*x.
Price for 3 tubs of popcorn: = 3*$6.75 = $20.25
Total price:
Pb(x) = $13*x + $20.25.
Now, we can find the number of friends x in such case that they will pay the same in each theater by:
Pa(x) = Pb(x)
$14.50*x + $17.25 = $13*x + $20.25.
Now we solve this for x:
($14.50 - $13)*x = $20.25 - $17.25 = $3
$1.50*x = $3
x = $3/$1.50 = 2.
Then, if there are 2 friends, they will pay the same in both theatres
If there are more tha 2 friends, the cheaper place will be Theatre B, because the slope is smaller, which means that for each additional ticket the total price will increase less.
