Tickets to the fair cost $8 for children and $15 for adults on thursday 177 people enter the fair and they collected $2053. what number of the children and what number of adults attended?

So,

Let

number of children tickets bought = c
number of adult tickets bought = a

We can now say that
c + a = 177
8c + 15a = 2053
because if you multiply c by the cost per child and a by the cost per adult, you will get the total revenue generated by all the tickets.

We now have a system of equations which can be solved by elimination (substitution).

Subtract a from both sides of the first equation.
c = 177 - a

Substitute 177 - a for c in the second equation.
8(177 - a) + 15a = 2053

Distribute.
1416 - 8a + 15a = 2053

Collect Like Terms.
1416 + 7a = 2053

Subtract 1416 from both sides.
7a = 637

Divide both sides by 7.
a = 91

Substitute 91 for a in the first modified equation.
c = 177 - 91
c = 86

Check.

The total number of people was 86 + 91 = 177 people.

The total revenue generated was 8(86) + 15(91) = 688 + 1365 = $2053.

There were 86 children and 91 adults.