Cansu's Tokens: Finding Possible Amounts Under 50

by TextBrain Team 50 views

Hey guys! Let's dive into a fun math problem about Cansu and her awesome token collection. Cansu is a super organized person, and she loves counting her tokens in different ways. She noticed something cool: she can count her tokens perfectly in groups of three, and also in groups of four, without any leftovers. The big question is, if Cansu has less than 50 tokens, what are the possible numbers of tokens she could have?

Understanding the Problem

So, the heart of the matter lies in finding numbers that are multiples of both 3 and 4. These numbers must also be less than 50. To solve this, we need to identify the common multiples of 3 and 4. The least common multiple (LCM) of 3 and 4 is 12. This means the numbers we are looking for must be multiples of 12. Essentially, Cansu's token count must be divisible by both 3 and 4, and under the 50 mark. Think of it like arranging tokens in neat little rows of 3 or 4 with no stragglers!

Finding the Multiples

Let’s list the multiples of 12 that are less than 50: 12, 24, 36, and 48. Each of these numbers can be divided evenly by both 3 and 4. For example, 12 divided by 3 is 4, and 12 divided by 4 is 3. The same holds true for 24, 36, and 48. This is crucial because it satisfies the condition that Cansu can count her tokens in groups of three and four without any remainders. This step is all about pinpointing the numbers that fit perfectly into both the 'group of 3' and 'group of 4' criteria, ensuring our solution aligns with the problem's core requirements.

Possible Token Numbers

Therefore, the possible number of tokens Cansu could have are 12, 24, 36, and 48. Each of these numbers satisfies the conditions outlined in the problem. They are all multiples of both 3 and 4, and they are all less than 50. These are the only numbers that fit all the criteria, making them the exclusive possibilities for Cansu's token count. Understanding multiples and common divisors helps in solving these type of questions.

Verifying the Solution

To be absolutely sure, let's quickly check each number: 12 ÷ 3 = 4 and 12 ÷ 4 = 3, 24 ÷ 3 = 8 and 24 ÷ 4 = 6, 36 ÷ 3 = 12 and 36 ÷ 4 = 9, 48 ÷ 3 = 16 and 48 ÷ 4 = 12. All these divisions result in whole numbers, confirming that each of these token counts works for Cansu. Each number neatly fits into both groups, leaving no token behind. This meticulous verification step ensures the accuracy of our solution, providing a solid conclusion to the problem.

Problems like these are super important because they help us develop our problem-solving skills. Thinking about multiples and common divisors is a fundamental concept in math. When we break down a problem like this, we're not just finding an answer; we're learning how to approach mathematical challenges in a structured way. This kind of thinking is beneficial in many areas of life, not just in math class. Understanding multiples is also key for more advanced math topics!

Real-World Connections

The skills we use to solve this problem are applicable in real life. For example, imagine you're planning a party and need to buy snacks. If you want to make sure everyone gets the same amount and you're dividing snacks into groups, understanding multiples can help you figure out how many of each item to buy. Another example is organizing items in a store – you might want to arrange products in rows or columns, and knowing about common divisors can help you make sure each row or column has the same number of items. The more we practice the better we become, it might become a superpower!

Tips for Solving Similar Problems

  • Understand the Question: Read the problem carefully to identify what is being asked.
  • Identify Key Information: Determine the important details, such as the number of tokens being less than 50.
  • Use Mathematical Concepts: Apply relevant concepts like multiples, common divisors, and least common multiple (LCM).
  • List Possible Solutions: Generate a list of potential answers that meet the criteria.
  • Check Your Work: Verify each solution to ensure it meets all the conditions of the problem.

Want to keep the math magic flowing? Try these problems:

  1. Problem 1: David is organizing his books. He can arrange them in stacks of 5 or 7 with no books left over. If David has fewer than 80 books, how many books could he have?
  2. Problem 2: A bakery is packaging cookies. They can put the cookies in boxes of 6 or 8 with no cookies remaining. If they have fewer than 100 cookies, what are the possible numbers of cookies they could have?
  3. Problem 3: Maria is making bracelets. She can use beads in sets of 4 or 9 with no beads left over. If Maria has fewer than 60 beads, how many beads could she have?

Conclusion

So there you have it! Cansu could have 12, 24, 36, or 48 tokens. Math can be pretty fun when we look at it like a puzzle! By understanding the basics of multiples and common divisors, we can solve a variety of problems, and we can also find connections between math and everyday life. Keep practicing and exploring, and you'll become a math whiz in no time! Keep up the great work, everyone!