During a recent survey of two middle school classrooms, 1/3 of the students reported that they bring their lunch to school. Another 1/4 reported that they buy their lunch in the cafeteria and 1/6 reported going home for lunch. The remaining 18 students reported that they don't eat lunch. How many students are in the two classes?

Question

During a recent survey of two middle school classrooms, 1/3 of the students reported that they bring their lunch to school. Another 1/4 reported that they buy their lunch in the cafeteria and 1/6 reported going home for lunch. The remaining 18 students reported that they don't eat lunch. How many students are in the two classes?

Answer 1

Let's start by finding the fraction of students who bring their lunch:

1/3 of the students bring their lunch.

Now let's find the fraction of students who buy their lunch:

1/4 of the students buy their lunch.

And the fraction of students who go home for lunch:

1/6 of the students go home for lunch.

We can add these three fractions together to find the fraction of students who eat lunch in some way:

1/3 + 1/4 + 1/6 = 6/12 + 3/12 + 2/12 = 11/12

This means that 1/12 of the students don't eat lunch (since 11/12 + 1/12 = 1). We can use this information to set up an equation:

18 = (1/12)x

where x is the total number of students. Solving for x, we get:

x = 216

So there are 216 students in the two classes.

Answer 2

Let's start by finding the fraction of students who bring their lunch to school. We are told that 1/3 of the students bring their lunch.

Let's represent the total number of students in the two classes as x.

So, the number of students who bring their lunch is 1/3 * x.

Now, let's find the fraction of students who buy their lunch in the cafeteria. We are told that 1/4 of the students buy their lunch.

So, the number of students who buy their lunch is 1/4 * x.

Next, let's find the fraction of students who go home for lunch. We are told that 1/6 of the students go home for lunch.

So, the number of students who go home for lunch is 1/6 * x.

Finally, we are told that 18 students reported that they don't eat lunch.

Therefore, the equation to represent the problem is:

1/3 * x + 1/4 * x + 1/6 * x + 18 = x

To solve this equation, we need to find a common denominator for the fractions.

The common denominator for 3, 4, and 6 is 12.

Multiplying the equation by 12, we get:

4x + 3x + 2x + 216 = 12x

Combining like terms, we have:

9x + 216 = 12x

Subtracting 9x from both sides, we get:

216 = 3x

Dividing both sides by 3, we have:

x = 72

Therefore, there are a total of 72 students in the two classes.