Question

A local venue is selling tickets to a show. They are selling $10 and $15 tickets, each with different seating. If the venue sells 1,000 tickets and collects a total of $12,200 from sales, how many of each type of ticket did they sell? Please explain the work

Answer 1

The local venue sold 560 tickets at $10 each and 440 tickets at $15 each. This was determined by setting up a system of linear equations based on the total tickets sold and the total revenue, and then using the elimination method to solve for the number of each type of ticket.

Step-by-step explanation:

To solve the problem of determining how many of each type of ticket were sold by the local venue, we can set up a system of linear equations. We are given two types of tickets: $10 tickets and $15 tickets. The venue sells a total of 1,000 tickets, which gives us our first equation:

Let x be the number of $10 tickets and y be the number of $15 tickets.

Equation 1: x + y = 1,000

The total amount of revenue collected from selling these tickets is $12,200, leading to our second equation:

Equation 2: 10x + 15y = 12,200

To find the values of x and y, we can use either substitution or elimination method. Let's use the elimination method in this case. To eliminate one of the variables, we can multiply Equation 1 by 10 and subtract it from Equation 2:

10(x + y) = 10(1,000)

10x + 10y = 10,000

Now subtract this result from Equation 2:

(10x + 15y) - (10x + 10y) = 12,200 - 10,000

5y = 2,200

Dividing both sides by 5:

y = 440

To find x, we substitute the value of y into Equation 1:

x + 440 = 1,000

x = 1,000 - 440

x = 560

Therefore, the venue sold 560 tickets at $10 and 440 tickets at $15.

Answer 2

Let $10 tickets be (x)

Let $15 tickets be (y)

Now we know they sold 1000 tickets

And they earned 12,200 from sales

So we can say

X+Y=1000

10x+15y=12,200

We can do substitution

So lets find Y first

Y=1000-x (basically x+y=1000 but solved for Y)

10x+ 15 ( 1000-x)= 12,200

You’d get

10x+15000-15x=12200

Combine and solve for x and you’ll get

x=560

So we know that x is 560

We can just use that to solve for Y

Since X is 560 tickets

And 1000 tickets soled

1000-560=440

440 ($15) tickets

560 ($10) tickets