Sixth Grade Lunchtime: A Math Problem!
Hey everyone, let's dive into a fun math problem! We're talking about sixth graders and their lunchtime choices. The question is, how many students are in the sixth grade in total? We've got some clues to help us solve it. Let's break it down step-by-step so you can easily understand and learn how to solve it yourself! This problem is a classic example of how percentages and basic math skills come together to solve real-world scenarios. It's not just about crunching numbers; it's about understanding how parts relate to a whole. So, grab your pencils, and let's get started. By the end, you'll be able to tackle similar problems with confidence. The ability to solve percentage problems is super useful in everyday life, from calculating discounts to understanding statistics.
Understanding the Problem
Alright, so here's the deal: On Monday, the sixth-grade students had a choice: buy lunch or bring lunch from home. We know a few key pieces of information. First, we know that 24% of the students purchased their lunch. Next, we're told that 190 students brought their lunch from home. The big question is: How many sixth-grade students are there in total? It's like a puzzle where we have to use the information we have to find the missing piece. This type of problem is super common in math. The key is to see how the percentage relates to the number of students who brought lunch. This means we'll need to figure out what percentage of the students brought their lunch from home. Then, we can use that information to find the total number of students. Remember, percentages are just a way of expressing a part of a whole, specifically a fraction of 100.
To begin with, we need to know what percentage of the students brought their lunch. If 24% bought lunch, then the rest of the students must have brought their lunch. The total percentage must always add up to 100%. Therefore, the percentage of students who brought their lunch is 100% - 24% = 76%. Understanding the problem is the most important step in the process. Ensure you clearly understand what information you are given and what you need to find. This also prevents you from making silly mistakes. Taking the time to understand the problem is not a waste of time!
Solving the Problem: Step-by-Step
Okay, let's get down to business and solve this problem! We know that 76% of the students brought their lunch, and that number represents 190 students. We can then use this information to determine the total number of students. Think of it like this: 76% of the total number of students is equal to 190. To find the total, we need to do a bit of math. Since 76% of the students represent 190 students, we can write this as an equation: 0.76 * Total Students = 190. Remember that we must convert the percentage into a decimal by dividing the percentage by 100. So 76% becomes 0.76. Now we need to isolate the variable, which is Total Students. To do this, we need to divide both sides of the equation by 0.76. Our equation looks like this: Total Students = 190 / 0.76.
Now, do the calculation: 190 divided by 0.76 equals 250. This means there are 250 total students in the sixth grade. Therefore, the total number of sixth-grade students is 250. The key to solving this type of problem is to first figure out the percentage that corresponds to the known quantity, in this case, the number of students who brought their lunch. Then, use that information to calculate the total. Always double-check your work to ensure your answer makes sense. Check the reasonableness of your answer. Does the total number of students seem logical, given the information provided? If your answer is super high or very low, it's a good idea to go back and check your work. Math problems like this are great practice for real-world scenarios, so keep practicing.
Checking Our Work
Awesome, we've got an answer. But it's always smart to double-check our work to make sure it's correct! Let's make sure our answer makes sense and that we did everything right. We'll verify our answer by working backward and confirming that the given percentages and the number of students who brought their lunch align. We'll take our answer, 250 students, and calculate the number of students who bought lunch and brought lunch and see if they match the information we were given. First, we know that 24% of the students bought lunch. Let's calculate 24% of 250. This is done by multiplying 250 by 0.24 (24% as a decimal). That calculation gives us 60 students who bought lunch. Next, we know that 76% of the students brought lunch. Let's calculate 76% of 250. This is done by multiplying 250 by 0.76 (76% as a decimal). That calculation gives us 190 students who brought lunch.
This matches the information provided in the problem. So, 60 students bought lunch, and 190 students brought their lunch. To check our answer, let’s add the number of students who brought and bought lunch. 60 + 190 = 250. And that’s the total number of students in sixth grade! So, our answer of 250 students is correct. And there you have it, folks! We've successfully solved the problem. Always remember to check your work; it's a great habit to get into. That final check can catch any mistakes you might have made along the way. Congrats! You successfully solved your math problem and learned how to solve similar problems in the future. Now you're all set to tackle similar problems and boost your math skills. Keep practicing, and you'll become a math whiz in no time!