Problem 14 - Algebra 1

Question

Solve the percent problem. \(85 \%\) of 300 is what number?

Step-by-Step Solution

Answer

The number that represents \(85\%\) of 300 is 255.

Step 1: Translate the verbal problem into an equation

From the problem, it is known that 85 percent of 300 is an unknown number. This can be translated into the equation \(0.85 * 300 = x\). Here, \(0.85\) is the decimal equivalent of \(85\%\), while \(x\) represents the unknown number that we need to find.

Step 2: Solve the equation

Solving the equation \(0.85 * 300 = x\), we get \(x = 255\). Hence, \(85\%\) of 300 is 255.

Key Concepts

Understanding Percent Conversion

When you're working with percentages, the first thing you need to do is convert the percentage into a decimal. This is because in most mathematical equations, we work with decimals rather than percentages directly. To convert a percentage into a decimal, you simply divide the percentage by 100.
For example, with our problem of solving what 85% of 300 is, you first take the percentage, 85%, and convert it into a decimal by doing:

• 85% \( \rightarrow \) Divide by 100 \( \rightarrow \) 85/100 = 0.85

Now you have the decimal representation, 0.85, which you can use in your calculations. Once you have the decimal, you are ready to use it in your equations for further calculation.

Solving Equations

Equations are like a balance scale, and your job is to keep them balanced while solving for the unknown variable, which in this case is \( x \). We took the word problem and turned it into a mathematical equation:

• 0.85 * 300 = x

This equation states that 0.85 multiplied by 300 equals \( x \), where \( x \) is the unknown value we're trying to find. Solving the equation requires understanding the relationship between the numbers and performing legal operations that do not upset this balance.

Multiplication in Equations

The multiplication in equations like the one in our problem is all about applying the operation to find the unknown, \( x \). Here, multiplication involves taking the decimal 0.85 and multiplying it by 300. This step will give us the value of our unknown number:

• 0.85 * 300
  Perform the multiplication:
• First, multiply 85 by 300: 85 * 300 = 25500
• Since we originally converted 85% to 0.85, we need to remember to account for the decimal: 25500 * 0.01 = 255

By completing these steps, we find that \( x = 255 \). Therefore, 85% of 300 is 255. Using multiplication in this way shows how effective decimal conversion is for finding percentage values.