Question

A theatre contains 457 seats and the ticket prices for a recent play were ​$54 for adults and ​$17 for children. If the total proceeds were ​$14,984 for a​ sold-out matinee, how many of each type of ticket were​ sold?

Answer 1

Chidden tickets were 262 and adult tickets were 195 tickets

Explanation:

Let x = the number of children tickets

Let y = the number of adult tickets.

x + y = 457

17x + 54y = 14984

Use substitution

x + y = 457 Solve for y

y = 457 -x Substitute 457 -x for y in the equation 17x + 54y = 14984

17x + 54y = 14984

17x + 54(457 -x) = 14984 Solve for x Distributer the 54

17x + 24678 - 54x = 14984 Combine like terms

-37x = -9694 Divide both sides by -37

x = 262

The number of children tickets.

x + y = 457 Substitute 262 for x and solve for y

262 + y = 457 Subtract 262 from both sides

y = 195

The number of adult tickets.

Helping in the name of Jesus.

Answer 2

Answer: 195 adult tickets and 262 children tickets

Explanation:

Let a be adult tickets and c be children tickets.

We know there are 457 seats.

a + c = 457

We also know the cost of the tickets and how much money was made.

$54a + $17c = $14,984

Now, we have a system of equations we can use to solve.

a + c = 457

$54a + $17c = $14,984

Lastly, we will graph this system, see attached. The point of intersection, or where the lines intersect, is our answer.

195 adult tickets and 262 children tickets.