Let the variables a and c to represent the number of adult tickets sold and the number of children’s tickets sold respectively.
From the information given,
Total number of tickets sold is 178
Thus,
x + y = 178
They charged $17.00 for an adult ticket and $9.00 for a child’s tickets. This means that the cont of x adult tickets is 17x and the cost of y child tickets is 9y.
Given that the total revenue ia $2,114.00, it means that
17x + 9y = 2114
The system of equations that describes the situation is
x + y = 178
17x + 9y = 2114
From the first equation,
x = 178 - y
Substituting x = 178 - y into 7x + 9y = 2114, we have
17(178 - y) + 9y = 2114
By expanading the parentheses on the left, we have
3026 - 17y + 9y = 2114
- 17y + 9y = 2114 - 1246
8y = 868
y = 898/8 = 449
x = 178 - y = 17