Question

Translate to an equation and solve. \(110 \%\) of what number is \(251.35 ?\)

Short answer

Answer: 228.50

Step-by-step solution

Set up the equation

We need to find a number (\(x\)) that when multiplied by 110% (or 1.1 as a decimal) equals 251.35. We can represent this with the equation: 1.1x = 251.35

Solve for x

To find the number \(x\), we need to get it alone on one side of the equation. Since x is being multiplied by 1.1, we can divide both sides of the equation by 1.1 to isolate \(x\): \( x = \frac{251.35}{1.1} \) Now, we can perform the division: \( x \approx 228.50 \)

Check the result

To make sure we have the correct number, we can multiply 228.50 by 110% (1.1) to see if the result is 251.35: \( 228.50 * 1.1 \approx 251.35 \) Since our result is close to 251.35 (with minor rounding differences), we have found the correct number. So, \(110\%\) of \(228.50\) is \(251.35\).

Key concepts

Equation Solving

When dealing with percentages and variables, setting up an equation is the first crucial step. An equation is essentially a mathematical statement that shows the relationship between different values. In this particular exercise, we need to find the unknown number (represented here as \(x\)) given that 110% of this number equals 251.35. To create the equation, think of the phrase "110% of what number is 251.35?".

• "110% of what number" translates to multiplying the unknown number \(x\) by 1.1 (since 110% as a decimal is 1.1).
• The phrase "is" often denotes equality in equations, so we place an equals sign (\(=\)) between this term and 251.35.

This becomes the equation: \(1.1x = 251.35\). Creating the correct equation is fundamental because it acts as your guide to find the missing number.

Decimal Conversion

Converting percentages to decimals is a key step in solving many mathematical problems. A percentage is a way of expressing a number as a fraction of 100, which makes it vital to understand how to convert it into a format that is easier to work with in equations. Here's how you can convert percentages to decimals:

• Take the percentage number and divide it by 100.
• For example, to convert 110% to a decimal, divide 110 by 100, resulting in 1.1.

This conversion means you can rewrite operations with percentages in simpler terms using decimal form, making calculations easier and more accurate, especially with multiplication or division involved.

Multiplication and Division

Once the equation is set up, the next steps usually involve multiplication or division to solve for the unknown variable. When you have an equation such as \(1.1x = 251.35\), solving for \(x\) means you'll need to perform inverse operations to isolate the variable.There are two main steps:

• Division: Since \(x\) is multiplied by 1.1, you'll divide both sides by 1.1 to isolate \(x\). This will look like: \(x = \frac{251.35}{1.1}\).
• Multiplication: Once you've calculated \(x\), check your result by reversing the process. Multiply your \(x\) value by 110% (or 1.1) to ensure it equals 251.35. This confirms your solution's accuracy.

These operations are integral parts of algebra, helping you solve equations and verify your results. Understanding these processes makes tackling many different types of problems possible.