Question

There is an unknown number of students at the beginning of lunch. Then each student has 4 friends come sit with them, tripling the amount. When the bell rings, most of the students leave the lunchroom. 1/4 of the students stay to finish their lunches. 8 students join the students who are still in the lunchroom. The total number of people in the lunchroom now is 22. Create and equation that correctly represents the story above and can be used to find the number of students in the lunchroom at the beginning of lunch.

Answer 1

We'll use the variable "x" to represent the unknown number of students at the beginning of lunch.

Step 1: Initially, there are x students.

Step 2: Each student has 4 friends join them, tripling the number of students. So, after this step, there are 4x students in the lunchroom.

Step 3: When the bell rings, 1/4 of the students stay, while the rest leave. So, (1/4) * 4x = x students stay, and the others leave. After this step, there are x students remaining in the lunchroom.

Step 4: 8 more students join those who are still in the lunchroom. So, the total number of people in the lunchroom is x (those who stayed) + 8 (those who joined) = x + 8.

According to the information given, the total number of people in the lunchroom now is 22. So, we can create the equation:

x + 8 = 22

Now, you can solve this equation to find the initial number of students (x):

x = 22 - 8

x = 14

So, there were 14 students in the lunchroom at the beginning of lunch.