Candy Sharing: How Many Each Friend Gets?
Hey guys! Let's dive into a sweet problem about sharing candies. It sounds like something we've all encountered, right? Figuring out how to divide treats equally is a classic puzzle, whether itâs for a party, a classroom, or just among friends. Today, weâre going to tackle a specific scenario that involves Ana, her candies, and a varying number of friends. So, grab your thinking caps, and letâs get started!
Setting Up the Sweet Scenario
So, Ana has a bunch of candies, and she wants to share them equally among her friends. In the first scenario, Ana has 15 friends. If she decides to share her candies among these 15 friends, each friend will get 8 candies. This gives us a starting point to figure out the total number of candies Ana has. We can easily calculate this by multiplying the number of friends by the number of candies each friend receives. Itâs a simple multiplication problem that helps us understand the total quantity of candies weâre working with.
Now, what happens if the number of friends changes? That's where the problem gets a little more interesting. Instead of having 15 friends, Ana now has 10 friends. The big question is: if she still wants to share all her candies equally, how many candies will each of these 10 friends get? This is a classic division problem, but with a slight twist. We first need to know the total number of candies before we can figure out the new distribution. Understanding this shift in the number of friends is crucial to solving the problem correctly.
To recap, we know:
- When Ana has 15 friends, each friend gets 8 candies.
- We need to find out how many candies each friend gets when Ana has only 10 friends.
Understanding the relationship between the number of friends and the number of candies each friend receives is key to cracking this problem. We're essentially looking at how a fixed quantity (the total number of candies) is divided among a different number of people. This kind of problem pops up in many real-life situations, from dividing resources in a company to sharing food at a potluck. So, let's get those mental gears turning and figure out how many candies each of Ana's 10 friends will get!
Calculating the Total Number of Candies
Alright, the first step to solving this candy conundrum is figuring out just how many candies Ana has in total. Remember, if she shares the candies among 15 friends, each of them gets 8 candies. To find the total number of candies, we simply multiply the number of friends by the number of candies each friend receives. This is a straightforward multiplication problem, and it's the key to unlocking the rest of the puzzle.
The calculation looks like this:
Total number of candies = Number of friends Ă Candies per friend
In this case, itâs:
Total number of candies = 15 friends Ă 8 candies/friend
So, let's do the math: 15 multiplied by 8 equals 120. That means Ana has a grand total of 120 candies to share. Now that we know the total number of candies, we can move on to the next part of the problem: figuring out how many candies each friend gets when there are only 10 friends.
Knowing the total number of candies is crucial because it remains constant regardless of how many friends Ana is sharing with. Whether she has 15 friends or 10 friends, the total amount of candy stays the same. This is a key concept in solving the problem. Itâs like having a fixed pie that you can slice into different numbers of pieces. The size of each piece changes depending on how many slices you make, but the total amount of pie remains the same.
With this information in hand, we're now ready to tackle the next part of the problem. We know Ana has 120 candies, and she wants to share them among 10 friends. The next step is to divide the total number of candies by the new number of friends to find out how many candies each friend will receive. This will give us the answer weâre looking for and solve the sweet mystery of Ana's candy sharing adventure!
Dividing the Candies Among 10 Friends
Okay, now that we know Ana has a grand total of 120 candies, the next step is to figure out how many candies each friend will receive when she shares them among 10 friends. This is where division comes into play. We're going to divide the total number of candies by the number of friends to find out how many candies each friend gets. This is a simple division problem, but it's essential to solving the overall puzzle.
The calculation looks like this:
Candies per friend = Total number of candies Ă· Number of friends
In this case, itâs:
Candies per friend = 120 candies Ă· 10 friends
So, let's do the math: 120 divided by 10 equals 12. That means each of Ana's 10 friends will receive 12 candies. We've successfully solved the problem! By first figuring out the total number of candies and then dividing that number by the new number of friends, we were able to determine how many candies each friend gets.
This problem illustrates a fundamental concept in math: the relationship between multiplication and division. Multiplication helps us find the total when we know the number of groups and the size of each group. Division helps us find the size of each group when we know the total and the number of groups. Understanding this relationship is crucial for solving a wide range of math problems, from simple sharing scenarios like this one to more complex calculations in science and engineering.
So, to recap, when Ana shares her 120 candies among 10 friends, each friend gets 12 candies. This is more than the 8 candies each friend received when she shared them among 15 friends, which makes sense because there are fewer friends to share with. This solution highlights the importance of carefully reading the problem, identifying the key information, and using the correct mathematical operations to find the answer.
The Sweet Solution: 12 Candies Each
So, after all the calculations and careful consideration, we've arrived at the answer! If Ana decides to share her candies among 10 friends, each friend will receive 12 candies. This means that by decreasing the number of friends, the share of candies each friend receives increases. Itâs a simple concept, but itâs fundamental to understanding how division works.
Therefore, the correct answer is:
B) 12 candies
This candy-sharing problem is a great example of how math can be applied to everyday situations. Whether you're dividing candies among friends, sharing resources in a group project, or splitting the bill at a restaurant, the principles of multiplication and division are always at play. By understanding these concepts, you can solve a wide range of problems and make informed decisions in your daily life.
I hope you guys found this candy-sharing problem fun and informative. Remember, math is not just about numbers and equations; it's about problem-solving and critical thinking. By practicing these skills, you can become a more effective problem-solver in all areas of your life. So, keep practicing, keep exploring, and keep having fun with math!