Math Problem Statement

All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 20% of students brought their lunch. 39 students brought their lunch. How many students in total are in Ridgewood Junior High School?

Solution

The question asks to find the total number of students at Ridgewood Junior High School. Here's the important information from the problem:

  • 20% of students brought their lunch.
  • 39 students brought their lunch.

We can set up a proportion to find the total number of students in the school.

Let xx be the total number of students. Since 20% (or 20100\frac{20}{100}) of the total students equals 39 students, the equation is:

20100×x=39\frac{20}{100} \times x = 39

Now, solve for xx.

First, multiply both sides by 100 to get rid of the fraction:

20x=39×10020x = 39 \times 100

20x=390020x = 3900

Next, divide both sides by 20:

x=390020=195x = \frac{3900}{20} = 195

So, there are 195 students in total at Ridgewood Junior High School.

Would you like a more detailed explanation or help with something else? Here are 5 related questions you might find useful:

  1. How do you solve for percentages in other types of problems?
  2. What happens when the percentage is unknown, but you know the total and a part?
  3. Can you find how many students didn’t bring their lunch?
  4. How would the problem change if 25% of the students brought lunch instead?
  5. How can you use a different method, such as ratio reasoning, to solve this?

Tip: When solving percentage problems, always check if converting the percentage to a fraction helps simplify the equation!

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Math Problem Analysis

Mathematical Concepts

Percentage
Proportion

Formulas

Percentage formula: (Part / Whole) * 100 = Percentage
Proportion formula: (Part / Whole) = Percentage / 100

Theorems

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Suitable Grade Level

Middle School