Solve: 5.9 X ? = 73.16 - Find The Missing Number!

Let's dive into solving this math problem step-by-step. Our main goal is to find the missing number that, when multiplied by 5.9, gives us 73.16. This kind of problem often appears in basic algebra and is a great way to sharpen your math skills. To begin, we need to understand the equation: 5.9 \times ? = 73.16. The question mark represents the unknown value we're trying to find. To isolate this unknown value, we need to perform the inverse operation of multiplication, which is division. In other words, we will divide both sides of the equation by 5.9. This isolates the unknown value on one side of the equation, allowing us to calculate its value. So, let's proceed with the division: ? = 73.16 / 5.9.

Step-by-Step Solution

To accurately solve for the unknown value, careful division is key. By dividing 73.16 by 5.9, we follow a standard long division or calculator-based approach. Let's perform the division: 73.16 ÷ 5.9 = 12.4. This calculation shows that the missing number is 12.4. To verify our answer, we can multiply 5.9 by 12.4 and check if it equals 73.16. So, 5.9 \times 12.4 = 73.16. This confirms that our solution is correct. Therefore, the missing number that satisfies the equation is indeed 12.4. Now, let's compare our solution with the options given: A. 0.124, B. 1.24, C. 12.4, D. 124. Clearly, option C, which is 12.4, matches our calculated value. Hence, the correct answer is C. This exercise highlights the importance of understanding basic algebraic principles and the relationship between multiplication and division. It also emphasizes the need for accuracy in performing calculations to arrive at the correct solution. By breaking down the problem into smaller steps and carefully executing each step, we can confidently solve such mathematical equations.

Why This is Important

Understanding how to solve equations like this is fundamental in mathematics. These skills are not only essential for academic success but also have practical applications in everyday life. Whether you're calculating expenses, determining proportions in cooking, or solving problems in various fields like engineering or finance, the ability to manipulate equations and find unknown values is invaluable. Moreover, practicing these problems enhances your problem-solving abilities and logical thinking, which are beneficial in any career or situation. So, keep honing your math skills and remember that every problem is an opportunity to learn and grow. Correct answer is C. 12.4.

Detailed Analysis of Options

Let's examine each option to understand why only one of them is the correct solution. This detailed analysis will reinforce your understanding of the problem and the process of solving it. Firstly, let's consider option A, which is 0.124. If we multiply 5.9 by 0.124, we get a result significantly smaller than 73.16. Specifically, 5.9 \times 0.124 = 0.7316. This is far from the target value, indicating that option A is incorrect. Secondly, let's evaluate option B, which is 1.24. Multiplying 5.9 by 1.24 gives us 5.9 \times 1.24 = 7.316. Although this result is closer to 73.16 than option A, it is still significantly off, making option B incorrect as well. Thirdly, option C, which is 12.4, is the one we identified as the correct answer through our step-by-step solution. As we confirmed earlier, 5.9 \times 12.4 = 73.16, which perfectly matches the target value. Lastly, let's analyze option D, which is 124. Multiplying 5.9 by 124 results in 5.9 \times 124 = 731.6. This value is ten times larger than our target value, clearly indicating that option D is incorrect. By examining each option and performing the multiplication, we can definitively conclude that only option C, 12.4, provides the correct solution to the equation. This comprehensive analysis not only helps in understanding why the other options are wrong but also reinforces the importance of accurate calculations and attention to detail in solving mathematical problems.

Practical Applications

Understanding and solving equations like 5.9 \times ? = 73.16 has numerous practical applications in everyday life and various professional fields. These skills are fundamental in scenarios where proportional reasoning and calculations are required. In personal finance, for example, you might use similar calculations to determine the cost of purchasing multiple items at the same price. Imagine you want to buy several items that each cost $5.9, and you have a total budget of $73.16. By solving the equation, you can quickly figure out how many items you can afford. In cooking, recipes often require adjusting ingredient quantities based on the number of servings. If a recipe for a certain dish uses 5.9 units of a particular ingredient and yields a total of 73.16 units of the final product, you can use similar calculations to scale the recipe up or down to suit your needs. In retail, understanding proportional relationships is crucial for calculating discounts, markups, and sales prices. For instance, if an item originally costs $73.16 and is being sold at a discount equivalent to 5.9 units, you can determine the discounted price using similar algebraic principles. In fields like engineering and construction, these skills are essential for scaling blueprints, calculating material requirements, and ensuring structural integrity. For example, if a construction project requires 5.9 units of a particular material per section and the total material needed is 73.16 units, engineers can use similar calculations to determine the number of sections that can be built. These examples illustrate the broad applicability of solving simple algebraic equations in various real-world contexts. Mastering these skills not only enhances your mathematical proficiency but also empowers you to make informed decisions and solve practical problems efficiently.

Conclusion

In conclusion, the solution to the equation 5.9 \times ____ = 73.16 is 12.4. This was determined by dividing 73.16 by 5.9, which isolates the unknown value. By verifying our answer through multiplication and comparing it with the given options, we confirmed that option C, 12.4, is the correct solution. This exercise underscores the importance of understanding basic algebraic principles and the relationship between multiplication and division. It also highlights the need for accuracy in performing calculations to arrive at the correct solution. Equations like these have practical applications in various fields, from personal finance and cooking to retail and engineering, making the ability to solve them a valuable skill. Keep practicing and honing your math skills to tackle more complex problems with confidence! To deepen your understanding of mathematical problem-solving, consider exploring resources like Khan Academy for additional lessons and practice exercises.