Solve for the base. Note: Round to the nearest hundredth. 800 is $4 \frac{1}{2}\%$ of what number?
Answer (2)
Convert the percentage to a decimal: 4 2 1 % = 4.5% = 0.045 .
Set up the equation: 800 = 0.045 x .
Solve for x : x = 0.045 800 = 17777.7777...
Round to the nearest hundredth: x = \tboxed 17777.78 .
Explanation
Understanding the Problem We are given that 800 is 4 2 1 % of some base, and we need to find that base. Let's denote the base by x . The problem states that 800 is equal to 4 2 1 % of x .
Converting Percentage to Decimal First, we need to convert the percentage 4 2 1 % to a decimal. We know that 4 2 1 = 4.5 , so 4 2 1 % = 4.5% . To convert a percentage to a decimal, we divide by 100. Therefore, 4.5% = 100 4.5 = 0.045 .
Setting up the Equation Now we can set up the equation: 800 = 0.045 x . To solve for x , we need to divide both sides of the equation by 0.045: x = 0.045 800
Solving for the Base Now, we perform the division: x = 0.045 800 = 17777.7777... We are asked to round the answer to the nearest hundredth, so we round 17777.7777... to 17777.78.
Final Answer Therefore, the base is approximately 17777.78.
Examples
Understanding percentages is crucial in everyday financial calculations. For example, if you want to calculate the sale price of an item that is 4.5% off and the discount is $800, you can use the same method to find the original price of the item. This is also applicable when calculating interest rates on loans or investments, helping you understand the actual cost or return.
To find the base, we determined that 800 is 4 2 1 % of some number, expressed it as an equation, and arrived at the base amount being approximately 17777.78. This was calculated by converting the percentage to a decimal and solving the equation. The final result is rounded to the nearest hundredth.
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