140 of what number is 308

less than a minute read 23-02-2025

Finding an unknown number when you know a percentage of it is a common mathematical problem. Let's explore how to solve the question: "140% of what number is 308?" We'll cover several methods, making it clear for everyone.

Understanding the Problem

The core of this problem is translating the sentence into a mathematical equation. "140% of what number is 308" can be written as:

140% * x = 308

Where 'x' represents the unknown number we're trying to find.

Method 1: Using Algebra

This is the most direct approach. We'll solve the equation for 'x':

Convert the percentage to a decimal: 140% = 1.40
Rewrite the equation: 1.40 * x = 308
Isolate 'x': Divide both sides of the equation by 1.40:

x = 308 / 1.40
Calculate: x = 220

Therefore, 140% of 220 is 308.

Method 2: Using Proportions

Proportions offer another way to approach percentage problems. We can set up a proportion like this:

140/100 = 308/x

This reads as "140 is to 100 as 308 is to x".

Cross-multiply: 140 * x = 308 * 100
Simplify: 140x = 30800
Solve for x: x = 30800 / 140
Calculate: x = 220

Again, we find that x = 220.

Method 3: Working Backwards from the Percentage

Since 140% is more than 100%, we know the unknown number will be less than 308. We can think of this in steps:

Find 10%: Divide 308 by 14 to find 10% (308/14 ≈ 22). Note: This step provides an approximation useful for mental calculation or quick estimation.
Find 100%: Multiply the 10% value by 10 (22 * 10 = 220). The approximation is refined here.

This method provides a faster mental approach, and a good estimate. But for accurate calculation, the algebraic methods are essential.

Verification

Let's check our answer:

1.40 * 220 = 308

Our calculations are correct!

Conclusion

We've successfully determined that 140% of 220 is 308. Understanding different methods – algebraic, proportional, and the estimation approach – provides flexibility in solving percentage problems. Choosing the best method depends on your comfort level and the specific problem's complexity. Remember to always verify your answer!