Unlocking The Product: When Sum Equals 15

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Unlocking the Product: When Sum Equals 15

Hey math enthusiasts! Let's dive into a fun little puzzle today. We're given a simple but intriguing scenario: the sum of two numbers is 15. Our mission, should we choose to accept it, is to figure out the product of these numbers. This isn't just about crunching numbers; it's about understanding relationships and exploring the cool ways math works. So, grab your calculators (or your brainpower!), and let's get started. We'll break down the problem step-by-step, making sure everyone can follow along and enjoy the journey.

Understanding the Basics: Sum and Product

Alright, before we jump into the deep end, let's quickly refresh some basic concepts. In math, when we talk about the sum, we're referring to the result of adding two or more numbers together. For example, the sum of 2 and 3 is 5 (2 + 3 = 5). Simple enough, right? The product, on the other hand, is the result of multiplying numbers. So, the product of 2 and 3 is 6 (2 x 3 = 6). Got it? Great! Now, let's apply these ideas to our problem, where the sum is given, and we need to find the product. We know the sum of two numbers is 15, which means if we add them, we get 15. Our goal is to find those numbers and then multiply them to get the product.

Now, let's explore this with some examples. If one number is 7 and the other is 8, their sum is 15 (7 + 8 = 15). The product, then, would be 56 (7 x 8 = 56). But what if the numbers are different? What if they are 10 and 5? The sum is still 15, but the product is now 50 (10 x 5 = 50). This illustrates that even though the sum remains constant, the product changes depending on the individual numbers. Our task is to determine which pair of numbers, that add up to 15, yields the correct product from the options provided in the question. The challenge is to identify the specific number pairs that meet the condition and deduce their product value. The initial step is to identify different combinations of numbers that sum to 15 to assess their respective products. Understanding this principle is crucial, as it sets the foundation for our mathematical reasoning.

Possible Number Combinations That Sum to 15

Alright, let's roll up our sleeves and explore some number combinations that add up to 15. This is where it gets a bit like a game! The fun part of this problem is that there is more than one solution. Here are a few examples to get us started, each time showing pairs of numbers summing to 15:

  • 1 and 14: 1 + 14 = 15. The product of these numbers is 1 x 14 = 14.
  • 2 and 13: 2 + 13 = 15. The product of these numbers is 2 x 13 = 26.
  • 3 and 12: 3 + 12 = 15. The product of these numbers is 3 x 12 = 36.
  • 4 and 11: 4 + 11 = 15. The product of these numbers is 4 x 11 = 44.
  • 5 and 10: 5 + 10 = 15. The product of these numbers is 5 x 10 = 50.
  • 6 and 9: 6 + 9 = 15. The product of these numbers is 6 x 9 = 54.
  • 7 and 8: 7 + 8 = 15. The product of these numbers is 7 x 8 = 56.

As you can see, there are several possibilities! Each of these pairs gives us a different product. The best way is to look at the answers and find the one that corresponds to the product. From the above, we see that none of the answers match those product values.

Analyzing the Answers and Finding the Correct Product

Now, let's analyze the given answer options, which will help us solve the problem. Remember, we're looking for the product of the two numbers whose sum is 15. Our options are:

  • A) 30
  • B) 42
  • C) 60
  • D) 70

To find the correct answer, we need to find a pair of numbers that add up to 15 and multiply to give us one of these options. We can do this through a bit of trial and error (since, based on the previous examples, we know there's more than one possibility!). Let's examine our number combinations from the previous section to see if the values match.

Alternatively, we can systematically test the answer choices. For each option, we can try to find two numbers that sum up to 15 and whose product equals the answer choice. For example:

  • Option B) 42: Can we find two numbers that sum to 15 and give a product of 42? If we try 6 and 9 (which sum to 15), their product is 54. This does not work.
  • Option C) 60: Let's try to find numbers that multiply to 60. From our examples, we have 5 and 10, which sums to 15 with a product of 50. This does not work.
  • Option D) 70: The pairs 7 and 8 have a product of 56. This does not work.

By comparing the products with the provided answers, we find that the product value equals 56, which corresponds to numbers 7 and 8. So the correct answer is B. This strategy helps us methodically work through the problem and pinpoint the correct product by matching it with the provided options. Understanding the sum-product relationship, combined with a methodical approach, ensures we solve the problem accurately. This method is effective because it considers all possible pairs that sum to 15, providing a complete and accurate resolution.

Conclusion: The Answer Revealed!

So, after careful consideration, the correct answer is B) 42 (when you consider the numbers 6 and 9. Though not matching the number in the options provided in this case, the closest option based on the question is B) 42. In this case, 6 and 9 is the closest pair with a product value of 54. If we were to work this through, we would be looking for the numbers 6 and 9 as a pair, for which the product is 54. However, of the options, the nearest correct answer would be B) 42. I hope you enjoyed this quick mathematical journey! Keep practicing, and you'll become a pro at these problems in no time. If you have any questions or want to try another math puzzle, drop a comment below. Happy calculating, everyone!