Math word problem

Question

A school band performs a spring concert for a crowd of 600 people. The revenue for the concert is $3150. There are 150 more adults at the concert than students. How many of each type of ticket are sold?

Answer 1

A school band performs a spring concert for a crowd of 600 people. The revenue for the concert is $3150. There are 150 more adults at the concert than students. How many of each type of ticket are sold?

Word problems. Just hearing those two words together causes most peoples anxiety to increase. It doesn't have to be that way. I have 4 steps for you to follow that will help you tackle these problems. Let's begin

Step 1: READ THE PROBLEM!

That's it. Just read the problem. The only thing we want at this point is to understand what's going on and what we're being asked to find. Reading the problem, we learn the school's band had a concert for a lot of people. The concert made some money. There were more adults than students. We're being asked how many students and how many adults attended the concert. Notice I didn't mention any of the numbers. Not important at this time. We just want to understand what's going on and what's being asked for us to find.

Step 2: DEFINE YOUR VARIABLE(S)

The question of the problem not only defines our variable(s), but it also helps us determine how many variables we need. The question here is, "How many of each type of ticket were sold?" There are two types of tickets - adults and students. Pick a variable for each type. I suggest picking variables that closely represents the type of tickets. a and s works. So we have:

a = number of adult tickets sold

s = number of student tickets sold

Step 3: CREATE YOUR SYSTEM OF EQUATIONS

Now we re-read the problem for the numbers and convert the words into expressions that will eventually turn into equations. First sentence, "A school band performs a spring concert for a crowd of 600 people." A total of 600 people attended the concert. Using our variables, how do you represent this statement?

a + s = 600 a number of adults + s number of students equals total of 600 people in attendance

Next sentence, "The revenue for the concert is $3150." Since our variables are defined as number of people and nothing to do with money, we need to skim the rest of the problem looking for anything else with money involved. In this problem, no other mention of money is made. In this case, we ignore this sentence. This sentence is just filler. Nice to know, but unhelpful in answering the question.

Moving on, "There are 150 more adults at the concert than students." Be very careful here with the wording. The common mistake made here is make the equation something like a +150 = s Keep in mind that a > s To get a = s you have to subtract from a to get its value to equal s. So our equation is:

a - 150 = s subtract the 150 difference from the larger number a, or

a = s + 150 add the 150 difference to the smaller number s, or

a - s = 150 subtract the smaller number from the larger number to get the difference

Let's pick the second one, it's already solved for one variable and has addition rather than subtraction.

So we now have a system of equations:

a + s = 600

a = s + 150

Step 4: SOLVE YOUR SYSTEM OF EQUATIONS

Since the second equation is already solved in terms of one variable, the substitution method is already set up for us to use. Substitute the value of a in the second equation into the first equation

a + s = 600

s + 150 + s = 600 Substitution

2s + 150 = 600 Combine like terms

2s = 450 Subtract 150 from both sides

s = 225 Divide 2 from both sides

We solved for s, now solve for a. Use either of our equations. Pick the equation that looks easiest to use. That second equation looks simple, it's already "solved" for a.

a = s + 150

a = 225 + 150 Substitute value of s

a = 375

Not quite done. We started this problem with words, it's fitting we finish with words as well. It makes sense. If someone asked you how many quarters you have, you wouldn't answer with q = 3 would you?

Use our found values of a and s and the definition of each variable to write out your final answer.

a = number of adult tickets sold

s = number of student tickets sold

a = 375

s = 225

There were 375 adult tickets sold and 225 student tickets sold.

Check your answer to make sure they make sense and matches the information given in the problem.

Basically, plug our answers into both equations we created. If we get true statements from each equation, we're good If not, re-check the steps, something went wonky.

RECAP:

Step 1: READ THE PROBLEM to find out what's going on and what's being asked for us to find.

Step 2: DEFINE VARIABLES

a = number of adult tickets sold

s = number of student tickets sold

Step 3: CREATE SYSTEM OF EQUATIONS

a + s = 600

a = s + 150

Step 4: SOLVE SYSTEM OF EQUATIONS and check your answer

a = 375

s = 225

There were 375 adult tickets sold and 225 student tickets sold.

375 + 225 = 600 check

375 = 225 + 150 check

Answer 2

Let "a" be the number of adults at the concert and "s" be the number of students. Assuming that only adults and students attended, then a + s = 600 and we can also say that a = s + 150.

Putting these together, since a + s = 600 we can say:

(s + 150) + s = 600

2s + 150 = 600

2s = 450

s = 225

Then a = 225 + 150 = 375

Answer 3

Hi Lisa, this is a problem involving systems of equations.

For this problem you need to write two separate linear equations that have two variables (x and y).

The two variables represented are students (s) and adults (a).

The first equation represents the amount of the tickets sold to adults and students: a + s = 600

The second equation represents the fact that there are 150 more adults than students: s + 150 = a

Now we are solving the system: a + s = 600 and s + 150 = a

Because we are given an equation for the amount of adults (a), we can substitute s + 150 for a in the other equation: (s + 150) + s = 600

Combining like terms we get 2s + 150 = 600

-150 -150

2s = 450

Then we divide by 2 to solve for the amount of students: 450 ÷ 2 = 225 students

Now we can plug the amount of students in to one of the equations to solve for the amount of adults:

a = (225) + 150 , so the amount of adults is 375.

To check that your solution is correct you plug both answers in to both initial equations:

375 + 225 = 600 AND 225 + 150 = 375

This means that the amount of students at the concert is 225 and the amount of adults is 375