Question

PLS HELP BRAINLIEST

A local dinner theater sells adult tickets for $105 each and children's tickets for $60 each. For a certain show, the theater sells 84 tickets for a total of $7155. How many of each type of ticket were sold?

define the variables for this problem. what do x and y equal?

Answer 1

Answer: 105x + 60y &= 7155 \\

x + y &= 84

\end{align*} \]

Solving this system, you should find that \( x = 45 \) and \( y = 39 \).

So, in the context of the problem:

- \( x \) (the number of adult tickets sold) equals 45.

- \( y \) (the number of children's tickets sold) equals 39.

Answer 2

Answer:

47 adult tickets and 37 children's tickets were sold.

Step-by-step explanation:

Let's define the variables for this problem:

• Let $x$ be the number of adult tickets sold.
• Let $y$ be the number of children's tickets sold.

The problem states that the theater sells adult tickets for $105 each and children's tickets for 60 each.

The total revenue from ticket sales is $7155. We can express this information in an equation:

$105x + 60y = 7155$

This equation represents the total revenue from selling $x$ adult tickets and $y$ children's tickets.

The problem also mentions that the theater sells a total of 84 tickets. This gives us another equation representing the total number of tickets sold:

$x + y = 84$

Now, we have a system of two equations with two variables:

$\begin{cases} 105x + 60y = 7155 \quad \textsf{.... Equation 1}\\ x + y = 84 \quad \textsf{.... Equation 2}\end{cases}$

To solve the system of equations:

We can use either the substitution method or the elimination method. Here, let's use the elimination method.

We'll start by eliminating one variable from the system by multiplying one or both equations by a constant so that the coefficients of one variable become opposites.

First, we can eliminate $y$ by multiplying the second equation by 60 and the first equation by 1. This will allow us to cancel out $y$:

$\begin{cases} 105x + 60y = 7155 \\ 60x + 60y = 5040 \end{cases}$

Now, we subtract the second equation from the first:

$(105x + 60y) - (60x + 60y) = 7155 - 5040$

$105x - 60x + 60y - 60y = 2115$

$45x = 2115$

Now, we solve for $x$:

$x = \dfrac{2115}{45} \\\\ x = 47$

Now that we have found $x = 47$, we can substitute this value into one of the original equations to find $y$. Let's use the second equation:

$47 + y = 84$

$y = 84 - 47 \\\\ y = 37$

So, the solution to the system of equations is $x = 47$ and $y = 37$.

Therefore, 47 adult tickets and 37 children's tickets were sold.