Problem 73 - Elementary Algebra

Question

In the following exercises, translate and solve. \(800 \%\) of 2250 is what number?

Step-by-Step Solution

Answer

The number is 18000.

Step 1: Understand the problem

We need to find what number is 800% of 2250. This means we need to calculate 800% of 2250.

Step 2: Convert the percentage to a decimal

To convert 800% to a decimal, divide by 100. So, \( 800\text{\textpercent} = \frac{800}{100} = 8 \).

Step 3: Set up the equation

We need to find the number that is 8 times 2250. Therefore, the equation is: \( x = 8 \times 2250 \).

Step 4: Perform the multiplication

Multiply 8 by 2250 to find the number. So, \( x = 8 \times 2250 = 18000 \).

Step 5: Write the final answer

The number that is 800% of 2250 is 18000.

Key Concepts

percentage to decimal conversion

When working with percentages, it's often necessary to convert them into decimals. This simplifies calculations, especially in algebraic equations.
**To convert a percentage to a decimal,**
follow these steps:
1. **Divide by 100:** This is equivalent to moving the decimal point two places to the left.
2. **Result is the decimal form:** For example, to convert 800% to a decimal, you divide 800 by 100.
Hence, \(\frac{800}{100} = 8\). Simplifying percentages into decimals makes arithmetic operations more straightforward.

multiplication

Understanding multiplication is key to solving percentage problems involving conversion to a decimal. **Multiplication** is one of the four elementary operations in arithmetic.
**Steps to multiply two numbers:**
1. Identify the numbers you need to multiply. In our example, it's 8 and 2250.
2. Multiply the numbers directly: \( 8 \times 2250 \).
The result of the multiplication is 18000.
Multiplying correctly is important for accurately finding the solution to percentage problems, as it directly influences the outcome.

solving algebraic equations

Solving algebraic equations often involves setting up equations based on given word problems. In our example, we translated '800% of 2250' into an equation.Here’s a simplified process:
1. **Identify the variable:** Determine what you need to find. Here, it's the number that is 800% of 2250, represented by \( x \).
2. **Set up the equation:** Based on the problem statement, we know \( x = 8 \times 2250 \).
3. **Solve for the variable:** Carry out the required operations to find the value of \( x \).
In our case, multiplication gives \( x = 18000 \).
This methodical approach ensures clarity and precision in solving mathematical problems.