Math Problem: Finding Girls And Boys In A Class

Hey guys, let's dive into a cool math problem! This one's all about figuring out how many girls and boys are in a class. We've got some clues, and we'll use a bit of logic and maybe some simple algebra to crack the code. Ready? Let's get started!

Understanding the Problem: The Setup

Okay, so the problem tells us a few key things. First, there are a total of 25 students in the class. That's our starting point, our total. Then, things get a little trickier. We're told that if there were five fewer girls, their number would be one-third of the number of boys. This is the crucial relationship we need to work with. It's like a secret code that helps us unlock the solution. What we know is that the number of girls, reduced by 5, is equal to a third of the boys. It's all about setting up this relationship in a way that helps us find the values of both the number of boys and girls in the class. We need to translate these words into mathematical equations. We'll assign variables to the unknowns, in this case, the number of girls and the number of boys, so that we can easily solve this problem. Doing so will help us to simplify the problem into a format that allows us to find the solution. The most important thing here is to understand the language of the problem and to correctly translate it into algebraic equations. From there, we just need to solve the equations!

Before we jump into the math, it's super important to read the problem carefully. Sometimes, the way the problem is worded can be a bit of a head-scratcher. That's totally normal! Take your time, break it down, and make sure you understand what the problem is asking. Don't worry if it doesn't click right away; it often takes a few reads to fully grasp the information.

Setting Up the Equations: Translating Words to Math

Alright, time to get our math hats on! Let's translate the problem into some equations. This is where we use variables to represent what we don't know, which is the number of girls and the number of boys.

Let's say:

• g = the number of girls
• b = the number of boys

From the first part of the problem, we know that the total number of students is 25. So, we can write our first equation:

• g + b = 25

This simply means the number of girls plus the number of boys equals the total number of students. Simple enough, right?

Now, for the trickier part. The problem states, "If there were five fewer girls, their number would be one-third of the number of boys." This translates to:

• g - 5 = b / 3

This equation tells us that if we subtract 5 from the number of girls, we get one-third of the number of boys. This sets up the second equation, which we can solve together with the first to discover the number of girls and the number of boys in the class. These two equations together give us the perfect setup to solve the math problem using algebraic methods. It allows us to calculate exactly what we're looking for with no guesswork.

Solving the Equations: Finding the Answers

Now, for the fun part – solving the equations! We have two equations and two unknowns, which means we can solve this using different methods. I'll show you one way to do it. There are often multiple methods that can be used!

Let's use the substitution method. From our first equation (g + b = 25), we can express b in terms of g:

• b = 25 - g

Now, substitute this expression for b into our second equation (g - 5 = b / 3):

• g - 5 = (25 - g) / 3

To solve for g, let's get rid of the fraction by multiplying both sides of the equation by 3:

• 3 * (g - 5) = 25 - g
• 3g - 15 = 25 - g

Next, let's bring all the g terms to one side and the constants to the other:

• 3g + g = 25 + 15
• 4g = 40

Now, divide both sides by 4 to find g:

• g = 10

So, there are 10 girls in the class!

Now that we know the number of girls, we can find the number of boys using the first equation (g + b = 25):

• 10 + b = 25
• b = 25 - 10
• b = 15

So, there are 15 boys in the class! The problem is solved! We have now found all of the information requested.

Checking Your Work: Does It Make Sense?

It's always a good idea to check your work to make sure your answers make sense. Let's see if our answers fit the original problem.

• We found 10 girls and 15 boys. The total is 10 + 15 = 25. That checks out!
• If there were 5 fewer girls, there would be 10 - 5 = 5 girls. Is 5 one-third of the number of boys (15)? Yes, it is! 15 / 3 = 5.

Our answers fit the description provided in the problem, so we can be confident that our answers are correct. If you get an answer that doesn't fit the problem, it may be necessary to go back and check your work to find any mistakes. Remember, everyone makes mistakes! It is a part of the process and a good way to learn.

Conclusion: You Did It!

Congratulations, guys! We successfully solved the math problem. We found that there are 10 girls and 15 boys in the class. We used the information provided to set up equations, solve them, and check our answers. This approach can be used for many math problems that may seem tricky at first, so don't be afraid to take them on! Remember to break down the problem into smaller pieces, translate the words into equations, and solve systematically. And always check your work! Math problems are a great way to improve our critical thinking skills and keep our minds sharp. Keep practicing, and you'll get better and better at solving these types of problems. Now go show off your math skills!