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48 Is 60 Percent of What Number?
Have you ever come across a problem where you are given a percentage and need to find the whole number it is a part of? If so, you might have encountered a question like “48 is 60 percent of what number?” This type of problem is often found in mathematics and can be solved using simple algebraic equations. In this article, we will explore different methods to find the unknown number and provide a step-by-step guide to help you solve such problems. Additionally, we will address some common FAQs related to this topic.
Understanding Percentages:
Before diving into the specific problem, it is crucial to have a clear understanding of percentages. A percentage is a way of expressing a fraction or a proportion out of 100. It represents the relationship between a part and a whole. For example, if you have 60 percent, it means you have 60 out of 100 parts or 0.6 as a decimal.
Step-by-Step Guide to Find the Unknown Number:
Let’s now solve the problem at hand, which is “48 is 60 percent of what number?” Here’s a step-by-step guide to finding the unknown number:
Step 1: Set up the equation:
Let x represent the unknown number. Since we are given that 48 is 60 percent of this number, we can write the equation as follows:
48 = 0.6x
Step 2: Solve for x:
To find the value of x, we need to isolate it on one side of the equation. Divide both sides of the equation by 0.6:
48 / 0.6 = x
80 = x
Step 3: Interpret the result:
The unknown number we were looking for is 80. Therefore, 48 is 60 percent of 80.
Alternative Method – Proportions:
Another way to solve this problem is by using proportions. We can set up a proportion between the known percentage and the unknown number. In this case, the proportion would be:
48/100 = x/60
Cross-multiplying and solving the equation, we get:
48 * 60 = 100x
2880 = 100x
x = 28.8
However, since we are dealing with a whole number, we round the result to the nearest whole number, which is 29. Therefore, 48 is 60 percent of 29.
FAQs:
Q: Can this method be used for any percentage?
A: Yes, this method can be used for any percentage. The only change you would make is to replace the given percentage in the equation.
Q: Is there a quicker way to solve this type of problem?
A: The method presented in this article is one of the most straightforward ways to calculate the unknown number. However, for certain percentages, mental calculations or estimation techniques can be used to arrive at a reasonable approximation.
Q: What if the percentage is given as a decimal or a fraction?
A: If the percentage is given as a decimal, you can directly use that decimal value in the equation. For example, if the percentage is 0.75, the equation would be 48 = 0.75x. If the percentage is given as a fraction, convert it to a decimal before proceeding with the equation.
Q: Can I use a calculator to solve these problems?
A: While a calculator can provide the numerical solution, it is essential to understand the underlying concepts and methods to solve these types of problems. Relying solely on a calculator may hinder your ability to grasp the mathematical reasoning behind the solution.
Q: How can I check if my answer is correct?
A: To check your answer, multiply the unknown number you found by the given percentage. It should equal the initial value. In our example, multiplying 29 by 60 percent (0.6) gives us 17.4, which is close to the initial value of 48.
In conclusion, finding the unknown number when given a percentage is a common mathematical problem. By following the step-by-step guide provided in this article, you can confidently solve such problems. Remember, understanding percentages and using algebraic equations or proportions are the keys to finding the desired solution.
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