84 is 12% of what number

84 is 12% of what number

The Correct Answer and Explanation is :

The correct answer is: 700

To determine what number 84 is 12% of, we can use the formula for percentage, which states that:

[
\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100
]

In this scenario, we know that 84 is the “Part,” and we want to find the “Whole.” Let’s denote the “Whole” as ( x ). Thus, we can rewrite the formula as:

[
12 = \left(\frac{84}{x}\right) \times 100
]

To isolate ( x ), we first rewrite the equation to remove the percentage:

[
12\% = \frac{84}{x} \implies 0.12 = \frac{84}{x}
]

Next, we can cross-multiply to solve for ( x ):

[
0.12x = 84
]

Now, to find ( x ), we divide both sides by 0.12:

[
x = \frac{84}{0.12}
]

Calculating this gives:

[
x = 700
]

Thus, 84 is 12% of 700.

Explanation

This calculation illustrates how to convert a percentage into a proportion of a total value. Percentages are a way to express a number as a fraction of 100. When we say that 84 is 12% of a number, we are essentially looking for a total amount that, when multiplied by 12% (or 0.12), yields 84.

By using the formula for percentages, we derived an equation that allowed us to isolate the unknown total. Cross-multiplication is a valuable technique here, allowing us to shift terms and solve for ( x ) in a straightforward manner.

Understanding this process is crucial in various real-life applications, such as financial calculations, statistics, and data analysis, where percentages frequently represent important metrics. Being comfortable with manipulating percentages and proportions can enhance one’s analytical skills and improve decision-making in both personal and professional contexts. Thus, mastering this basic mathematical skill has broad implications and applications.