1474 concert tickets were sold for a total of ​$24,951. If students paid ​$13 and nonstudents paid ​$20​, how many student tickets were​ sold?

Answer 1

Let's try an easier problem first.

10 concert tickets were sold for a total of $38

students paid $2 and non-students paid $5

How many student tickets were sold?

We have to set up two equations using the information given.

The first piece of information is that 10 concert tickets were sold.

If we look for what else we know about concert tickets from the problem it says that there were student tickets and non-student tickets sold.

So our equation is

some number of student tickets plus some number of non-student tickets has to equal 10 tickets.

To turn this into an equation we say what our variable (letter that represents an unknown number) stands for

Let s = number of student tickets (if writing by hand make sure your s doesn't look like a 5. If it does, pick a different letter to use)

Let n = number of non-student tickets

s + n = 10

student tickets sold + non-student tickets sold = 10 tickets sold

Going back to the problem let's see if we can get a second equation. We also have information about money.

We know the total was $38 and that each student ticket is $2 and each non-student ticket is $5

So the number of student tickets sold times the cost of the ticket plus the number of non-student tickets sold x the cost of the non-student ticket has to equal 38

2s + 5n = 38

So now we have

s + n = 10

2s + 5n = 38

Step 1: Solve for one variable in the first equation. Let's solve for s

s + n = 10

-n - n

s = 10 - n

Step 2: Substitute what s is equal to into the second equation

s = 10 - n

2s + 5n = 38

Step 3: Solve for n

2(10 - n) + 5n = 38

20 - 2n + 5n = 38 Distribute

20 + 3n = 38 Combine like terms

-20 -20 subtract 20 from both sides

3n = 18 divide by 3

3 3

n = 6

but we aren't done yet. The question asks for the number of student tickets. We found the number of non-student tickets!

To solve for s use one of the equations you created and substitute the value you found for n

s + n = 10

s + 6 = 10

s = 4

Last step: Check using your other equation and the two values you found

2s + 5n = 38

s = 4 n = 6

2(4) + 5(6) = 38

8 + 30 = 38

38 = 38

Now you can try the harder problem on your own using the outlined steps.

For many people setting up the two equations is the hardest part.

First create the equation about concert tickets

Then create an equation about money

Feel free to reach out if you need more practice on how to do these types of problems!

Answer 2

s repesents the number of students

1474 - s represents the number of non-students

13s + 20(1474 - s) = 24951

Can you solve for s and answer?