Problem 71 - Elementary Algebra

Question

In the following exercises, translate and solve. \(250 \%\) of 65 is what number?

Step-by-Step Solution

Answer

162.5

Step 1: Convert Percentage to Decimal

To find 250% of 65, first convert 250% to a decimal. To do this, divide 250 by 100: 250% = \( \frac{250}{100} = 2.5\)

Step 2: Multiply the Decimal by the Number

Next, multiply the decimal by the number 65 to find 250% of 65: \(2.5 \times 65 = 162.5\)

Step 3: Write the Answer

Therefore, 250% of 65 is 162.5. The answer is 162.5.

Key Concepts

converting percentages to decimals

Converting percentages to decimals is the first essential step when working with percentage calculations. A percentage represents a number out of 100. To convert a percentage to a decimal, you need to divide the percentage value by 100. For example, to convert 250% to a decimal, you perform the operation:

• \( \frac{250}{100} \)
• Which simplifies to 2.5

Now, 250% is represented as 2.5 in decimal form. Converting percentages to decimals simplifies further calculations, especially multiplication, making solving math problems more straightforward.

multiplication

Once you have converted the percentage to a decimal, the next step is multiplication. Multiplication is the process of calculating the total of one number added repeatedly. In our example, we need to find 250% of 65.The decimal form of 250% is 2.5. The expression '250% of 65' translates to multiplying the decimal by the number 65. This calculation looks like:

• \( 2.5 \times 65 \)
• Which equals 162.5

Thus, the result of the multiplication tells us that 250% of 65 is 162.5. Understanding multiplication is crucial for efficiently solving percentage problems.

problem-solving steps

Breaking down complex problems into manageable steps is a helpful problem-solving strategy. Here are the steps to solve the exercise '250% of 65 is what number?':

• Step 1: Convert the percentage to a decimal: \(250\% = 2.5\)
• Step 2: Multiply the decimal by the given number: \(2.5 \times 65 = 162.5\)
• Step 3: State the final answer: 250% of 65 is 162.5

Following these steps ensures that you methodically handle each part of the problem, leading you to the correct answer. This systematic approach can be applied to similar percentage calculation problems, enabling you to tackle them confidently.