$ 8 for adults & $ 5 for seniors. 325 people paid, the total receipts were $ 2569. How many paid were adults? How many paid were seniors? //...

Let us assume that the number os adults =
x

And assume that the number os seniors =
y

We are given that total people paid  is
325.

==> x + y =
325

==> x= 325 - y
...........(1)

We are given that
:

cost for an adults =
8

==> total cost for adults = cost per adult * total
number of adults

                                       =
8*x

Cost for a senior =
5

==> total cost for seniors =
5*y

But total cost ( adults and seniors) =
2569

==> 8x + 5y = 2569
.........(2)

From (1), we will substitute in
(2):

==> 8(325-y) + 5y =
2569

==> 2600 - 8y + 5y =
2569

==> 2600 - 3y =
2569

==> 3y =
31

==> y= 31/3 = 10.33 which is impossible because
number of seniors should be an integer.

We will assume that
y= 10 and total cost where 2570

==>
total number of seniors =
10

        total number of
adults = 315.