62.4 percent of what number is 17.16
The correct answer and explanation is:
Correct Answer:
62.4% of 27.5 is 17.16.
Explanation (300 words):
To solve the problem “62.4 percent of what number is 17.16,” we need to set up a basic percentage equation. The word “of” in math typically means multiplication, and “is” translates to the equals sign. Here’s the step-by-step breakdown:
Step 1: Convert the Percentage to a Decimal
Percent means “per hundred.” So, to convert 62.4% to a decimal, divide by 100: 62.4%=62.4100=0.62462.4\% = \frac{62.4}{100} = 0.624
Step 2: Set Up the Equation
Let the unknown number be xx. The phrase “62.4% of what number is 17.16” becomes: 0.624×x=17.160.624 \times x = 17.16
Step 3: Solve for xx
To isolate xx, divide both sides of the equation by 0.624: x=17.160.624x = \frac{17.16}{0.624} x=27.5x = 27.5
Step 4: Check Your Work
Multiply 27.5 by 0.624 to verify: 0.624×27.5=17.160.624 \times 27.5 = 17.16
Correct!
Why This Works:
Understanding percent problems involves grasping the relationship between three values: the part, the whole, and the percentage. In this case, 17.16 is the part, 62.4% is the percentage, and we are solving for the whole.
We reversed the typical “find the percent” process. Instead of calculating what 62.4% of a number is, we already knew the result (17.16) and the percentage (62.4%). So, we worked backward to find the original number.
This method is widely used in real life, such as finding total costs from discounts, calculating population proportions, or reversing tax-inclusive prices to find the pre-tax value.
Understanding how to reverse percentages is essential for solving a broad range of practical math problems effectively.