Can you help me solve this word problem

Question

Dodd ms raised $860 from ticket sales for a concert. Tickets  sell for $2.50 in advanced & $4.00 at the door.If a total of 275 tickets are sold, how many tickets were sold at the door.

 

Answer 1

Hi Emani,

 

It looks like we're dealing with only two types of tickets: those sold in advance and those sold at the door. We'll come up with variables to represent how many of each ticket we sold:

 

     a = the number of advance tickets sold

     d = the number of door tickets sold

 

The problem tells us that we sold a total of 275 tickets, so:

 

     a + d = 275

 

The problem also tells us that we raised $860 from all of our sales, so:

 

     $860 = $2.50a + $4.00d

 

Here, we have a system of two equations with two unknowns. The problem asks us how many tickets were sold at the door, so we want to try and solve for d. In order to do that, we'll need to eliminate a from one of the equations. Let's work with the first equation by subtracting d from both sides:

 

     a = 275 - d

 

Now, we can plug this into the second equation, replacing a with (275 - d):

 

     $860 = $2.50(275 - d) + $4.00d

 

Distribute the $2.50 into the parenthesis:

 

     $860 = $687.50 - $2.50d + $4.00d

 

Let's combine the two d terms:

 

     $860 = $687.50 + $1.50d

 

Now, subtract $687.50 from both sides:

 

     $172.50 = $1.50d

 

And finally, divide both sides by $1.50 to obtain d.

 

 

I hope this has helped!