All students in Ridgewood Junior High School either got their lunch in the school cafeteria or brought it from home on Tuesday. $20\%$ of students brought their lunch. $41$ students brought their lunch. How many students in total are in Ridgewood Junior High School? $\newline$ Answer: $\square$

Full solution

Q. All students in Ridgewood Junior High School either got their lunch in the school cafeteria or brought it from home on Tuesday.

20\%

of students brought their lunch.

41

students brought their lunch. How many students in total are in Ridgewood Junior High School?

\newline

Answer:

\square

Understand Problem: Understand the problem and determine what is given and what needs to be found. $\newline$ We are given that $20\%$ of the students brought their lunch, which equates to $41$ students. We need to find the total number of students in the school.
Set Up Equation: Set up the equation to find the total number of students. $\newline$ If $20\%$ of students brought their lunch and that represents $41$ students, we can set up the equation: $\newline$ $20\%$ of Total Students = $41$
Convert to Decimal: Convert the percentage to a decimal to perform the calculation. $20\%$ as a decimal is $0.20$ . So the equation becomes: $0.20 \times \text{Total Students} = 41$
Solve for Total: Solve for the Total Students. $\newline$ To find the Total Students, we divide the number of students who brought their lunch by the decimal percentage. $\newline$ Total Students = $\frac{41}{0.20}$
Perform Division: Perform the division to find the total number of students. $\newline$ Total Students = $41 / 0.20 = 205$
Verify Solution: Verify the solution. $\newline$ If there are $205$ students in total and $20\%$ brought their lunch, then $0.20 \times 205$ should equal $41$ . $\newline$ $0.20 \times 205 = 41$ $\newline$ This confirms our solution is correct.