Michael Z. answered • 10/31/19
Mathematics Tutor
Note: I slightly changed the wording of this problem as it appears the original was a multiple choice answer.
A theater charges $5 for student tickets and $7 for adult tickets. They sold 75 tickets for a total of $425. Determine the number of student tickets and the number of adult tickets sold?
Step 1: Read the problem.
Do nothing else. We only want to get a general idea of the situation and what we are being asked to find.
Step 2: Define your variable(s)
The question at the end of the problem will help define our variables. I like to use variables that closely matches what we are trying to find. In this case, we need to find the number of student and adult tickets sold. So, let s=the number of student tickets sold and a=the number of adult tickets sold
Step 3: Set up your equation(s)
The number of equations you need to set up is the same as the number of variables you have. Since we have two variables, s and a, we will need two equations. Re-read the problem and use the information to create our equations.
The first thing we read is "A theater charges $5 for student tickets and $7 for adult tickets" Convert this into an algebraic expression representing the total amount a theater received from student and adult ticket sales. We get 5s (for $5 per student ticket sale) and 7a (for $7 per adult ticket sale. Add them together and we get the total amount the theater received from ticket sales
5s + 7a
The next line tells us we sold 75 tickets for a total of $425. Since our above expression deals with money, we will ignore the sold 75 tickets (for now) and complete our equation with a total of $425. So now we have our first equation:
5s + 7a = 425
We will create our second equation in the same fashion. We now come back to the "sold 75 tickets" that we previously ignored. Now we are talking about the number of tickets sold. By definition, our variables are the number of student and adult tickets sold. Add those two variables together and they equal 75. Our second equation is:
s + a = 75
We now have our two equations that form a system of equations.
5s + 7a = 425
s + a = 75
There are several ways we can use to solve this system of equations. They are graphically, substitution, and elimination. Given that at least one variable doesn't have a number in front of it, substitution would be the easiest method to use. The goal now is to solve one of the equations for one variable. Both variables of the second equation are by themselves, so pick one variable to solve. I choose to solve for s by subtracting a from both sides of the second equation. I now have:
s = 75 - a
Substitute our new value of s into the first equation.
5(75 - a) + 7a = 425 Solve for a
375 - 5a + 7a = 425 Distribution Property
375 + 2a = 425 Combine like terms
2a = 50 Subtract 300 from both sides
a = 25 We found the value of a
Now find the value of s by substituting the value of a in one of our equations above.
s = 75 - a
s = 75 - 25
s = 50
We now have a = 25 and s = 50. But are they correct? Check your answer by plugging our found values into each of our original equations. If we get true statements from each one, we are correct.
5s + 7a = 425 s + a = 75
5(50) + 7(25) = 425 50 + 25 = 75
250 + 175 = 425 75 = 75 TRUE
425 = 425 TRUE
WE DID IT!!!!
The theater sold 50 student tickets and 25 adult tickets.
P.S. If we had a list of multiple choices, we would have picked the one with our system of equations we created.
