if 26% of a number is 65 . find the number
The correct answer and explanation is:
To find the number when 26% of it equals 65, we can use the formula: Percentage value=(Percent100)×Number\text{Percentage value} = \left( \frac{\text{Percent}}{100} \right) \times \text{Number}
Given:
- Percent = 26%
- Percentage value = 65
Let the unknown number be xx. Then: 26% of x=65⇒(26100)×x=6526\% \text{ of } x = 65 \Rightarrow \left( \frac{26}{100} \right) \times x = 65 0.26x=650.26x = 65
Now solve for xx: x=650.26=250x = \frac{65}{0.26} = 250
✅ Correct Answer: 250
📘 300-Word Explanation:
This is a classic percentage problem where you’re given the percentage of a number and asked to find the original number. Here’s how to approach such problems step by step.
The problem states that 26% of a number is 65. That means if you take 26% of some unknown number, you end up with 65. In math, this is written as: 26100×x=65\frac{26}{100} \times x = 65
To remove the percentage, convert it to a decimal. The percentage 26% becomes 0.26 in decimal form. So the equation becomes: 0.26×x=650.26 \times x = 65
This is a simple algebraic equation. To isolate xx, divide both sides of the equation by 0.26: x=650.26x = \frac{65}{0.26}
Doing the division: x=250x = 250
This means that the original number must be 250 because 26% of 250 is: 0.26×250=650.26 \times 250 = 65
This type of problem is useful in real-life scenarios such as calculating discounts, tax, commissions, or interpreting test scores. Understanding how to reverse percentage operations—going from a known percent value back to the base number—is a valuable algebra skill. Always remember: “of” in math usually means multiplication, and converting percentages to decimals is essential in calculations.