10 is 30% of what number?
Solution:
Part:
whole
percent:
The Correct Answer and Explanation is :
To find out what number 10 is 30% of, we can set up a simple equation based on the definition of percentage.
Step-by-Step Solution
- Understanding Percentages: A percentage is a way of expressing a number as a fraction of 100. So, when we say 30%, it can be expressed as (\frac{30}{100}) or 0.30 in decimal form.
- Setting Up the Equation: Let’s denote the whole number we are looking for as (x). According to the problem, 30% of (x) equals 10. Mathematically, this can be expressed as:
[
0.30 \times x = 10
] - Solving for (x): To find (x), we need to isolate it. We can do this by dividing both sides of the equation by 0.30:
[
x = \frac{10}{0.30}
] - Calculating the Value: Performing the division:
[
x = \frac{10}{0.30} = \frac{10 \times 100}{30} = \frac{1000}{30} = 33.33\overline{3}
]
Thus, (x) is approximately 33.33.
Conclusion
10 is 30% of approximately 33.33.
Explanation of the Concept
Understanding percentages is crucial in many areas of life, including finance, statistics, and daily decision-making. The concept of percentage helps quantify how one number relates to another in terms of proportions. In this case, we were tasked with finding the whole from which a given percentage is derived. This process is foundational in mathematics and can be applied in various contexts, such as calculating discounts, determining tax rates, or interpreting data.
By isolating the variable (x) through algebraic manipulation, we can derive the total quantity (the whole) from a given fraction (the part). This principle can be extended to more complex calculations and is vital for comprehending ratios and proportions. Overall, mastering percentages enables us to make informed decisions based on numerical data in both personal and professional settings.