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.
