Translate and solve: 3984 is what percent of 24.9? Provide your answer below: _
The Correct Answer and Explanation is:
Translation and Solution:
Problem:
3984 is what percent of 24.9?
Translation into a mathematical equation:
Let xx be the percent value we want to find.
We translate “3984 is what percent of 24.9” into: x%×24.9=3984x\% \times 24.9 = 3984
Convert x%x\% to a decimal: x100×24.9=3984\frac{x}{100} \times 24.9 = 3984
Now solve for xx: x100=398424.9\frac{x}{100} = \frac{3984}{24.9} x100≈159.83735\frac{x}{100} \approx 159.83735 x≈15983.735x \approx 15983.735
Final Answer: 15983.735%\boxed{15983.735\%}
Explanation
Understanding percent problems involves recognizing the relationship between parts and wholes. The phrase “3984 is what percent of 24.9?” is asking: how many hundredths (or parts per hundred) of 24.9 equal 3984?
To solve this, we convert the word problem into a mathematical equation using basic percent concepts. In general, the structure is: Percent=(PartWhole)×100\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
In our case, the part is 3984, and the whole is 24.9. Plugging those into the formula: (398424.9)×100\left( \frac{3984}{24.9} \right) \times 100
This simplifies to: 159.83735×100=15983.735%159.83735 \times 100 = 15983.735\%
This means that 3984 is 15,983.735% of 24.9. The number seems unusually large, which is a good opportunity to reflect on why. Generally, percent values are often within the 0–100% range when dealing with everyday quantities. But in cases where the “part” (numerator) is much larger than the “whole” (denominator), the result is a percent value well over 100%.
In context, if you started with only 24.9 of something (say dollars) and ended up with 3984, you have increased your amount by over 159 times, or nearly 16,000% of the original value. This illustrates how percent can powerfully express large relative differences, which is especially useful in financial growth, population changes, or comparing vastly different quantities.
Thus, 3984 is 15,983.735% of 24.9.
