84 is 35% of what number?
The Correct Answer and Explanation is:
84=35% of X
Convert 35% to a decimal: 35%=35100=0.3535\% = \frac{35}{100} = 0.3535%=10035=0.35
Now the equation becomes: 84=0.35×X84 = 0.35 \times X84=0.35×X
To find XXX, divide both sides of the equation by 0.35: X=840.35=240X = \frac{84}{0.35} = 240X=0.3584=240
Correct answer: 240
Explanation
Solving percentage problems like “84 is 35% of what number?” requires understanding how percentages relate to whole numbers. A percentage represents a part out of 100. So, 35% means 35 out of every 100 parts. When a problem asks “84 is 35% of what number?”, it means 84 is a part of some unknown whole, and that part makes up 35% of the total.
We begin by expressing the percentage as a decimal to make calculations easier. To convert 35% to a decimal, divide 35 by 100, which gives 0.35. This is because percentages are per hundred, and working in decimal form simplifies multiplication and division.
Next, we set up the relationship as a mathematical equation: 84=0.35×X84 = 0.35 \times X84=0.35×X
This tells us that 35% of some number XXX equals 84. To isolate XXX, we perform the inverse operation—division: X=840.35X = \frac{84}{0.35}X=0.3584
Now, calculate this division: X=240X = 240X=240
This means that 84 is 35% of 240.
This method is applicable to any similar percentage problem. Always translate the percentage into a decimal and use multiplication or division to solve. It’s important in many real-life situations such as calculating discounts, taxes, test scores, or financial data. Understanding how to manipulate percentages helps in budgeting, business decisions, and interpreting data, making it a fundamental skill in both academic and daily contexts.
