Problem 25 - Elementary Algebra

Question

What percent is \(37.5\) of 1500 ?

Step-by-Step Solution

Answer

2.5%

Step 1: Understand the Percent Formula

The formula to find what percent one number is of another number is: \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] Here, the 'part' is 37.5 and the 'whole' is 1500.

Step 2: Set Up the Fraction

Substitute the values into the formula: \[ \text{Percent} = \frac{37.5}{1500} \]

Step 3: Calculate the Fraction

Divide 37.5 by 1500: \[ \frac{37.5}{1500} = 0.025 \]

Step 4: Convert to a Percentage

Multiply the result by 100 to get the percentage: \[ 0.025 \times 100 = 2.5 \]

Step 5: State the Result

37.5 is 2.5% of 1500.

Key Concepts

percent formula

To solve percentage problems, the percent formula is your go-to tool. The formula is: \[ \text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100 \] This helps to determine what portion one number (the part) is of another number (the whole).
For example, if you want to find out what percent 37.5 is of 1500, you set it up as follows:
\[ \text{Percent} = \frac{37.5}{1500} \times 100 \] Plugging the numbers into the formula helps you perform consistent calculations whenever dealing with percentages.

fractions

Understanding fractions is crucial for solving percentage problems. A fraction consists of a numerator (the top number) and a denominator (the bottom number).
In the percent formula, the 'part' is the numerator and the 'whole' is the denominator. For example, to find what percent 37.5 is of 1500, we write it as a fraction: \[ \frac{37.5}{1500} \]
Then, the fraction is converted by dividing the numerator by the denominator to get a decimal. This step is key because it transforms the fraction into a simpler form that we can easily multiply by 100 to find the percentage.

basic arithmetic

Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. These operations are foundational skills for solving percent problems.
When calculating what percent 37.5 is of 1500, we need to perform a few basic arithmetic steps:

• First, divide 37.5 by 1500 to get the decimal form: \[ \frac{37.5}{1500} = 0.025 \]
• Next, multiply the decimal by 100: \[ 0.025 \times 100 = 2.5 \]

By mastering these basic arithmetic operations, you can handle any percentage calculation confidently and accurately.