Problem 94 - Elementary Algebra

Question

Cherise deposits \(8 \%\) of each paycheck into her retirement account. Her last paycheck was \(\$ 1,485 .\) How much did Cherise deposit into her retirement account?

Step-by-Step Solution

Answer

Cherise deposited \$118.80 into her retirement account.

Step 1: Understand the Problem

The problem gives the percentage of Cherise's paycheck that is deposited into her retirement account and the amount of her last paycheck. The goal is to find out how much she deposited.

Step 2: Convert the Percentage to Decimal

Convert the percentage of the paycheck deposited into her retirement account (8%) into a decimal form. This is done by dividing the percentage by 100. \[ 8\text{\text{ \textpercent}} = \frac{8}{100} = 0.08 \]

Step 3: Multiply the Decimal with the Paycheck Amount

Multiply the decimal form of the percentage (0.08) by the amount of her last paycheck (\$1,485). \[ 0.08 \times 1,485 = 118.80 \]

Step 4: State the Result

The result of the multiplication is the amount Cherise deposited into her retirement account.

Key Concepts

decimal conversion

When we encounter percentages in problems, we often need to convert these percentages to decimals to make calculations easier. Percentages are out of 100, which means converting them to decimals is quite simple.

To convert a percentage to a decimal, follow this simple step:

• Divide the percentage number by 100.

For example, for Cherise's retirement contribution, the percentage value given is 8%. To convert this to a decimal: \[ 8 \text{ \textpercent} = \frac{8}{100} = 0.08 \] This gives us the decimal equivalent of 0.08. Using the decimal form can simplify our multiplication and help in solving many real-world problems.

retirement savings calculation

Planning and calculating retirement savings is important for financial stability in the future. One common method is to save a portion of each paycheck.

In Cherise's case, she is depositing 8% of each paycheck into her retirement account. The steps to find the amount deposited are:

• Determine the percentage of the paycheck to be saved.
• Convert the percentage to a decimal (as discussed previously).
• Multiply the decimal by the paycheck amount.

For Cherise:

• Her last paycheck was \(1,485.
• The percentage saved is 8%, which we converted to 0.08.
• Thus, the deposited amount is: \[ 0.08 \times 1,485 = 118.80 \]

This tells us Cherise deposited \)118.80 from her last paycheck into her retirement account. Small, consistent savings can lead to a significant amount over time, making such calculations essential.

multiplication with decimals

Understanding how to multiply with decimals is crucial for financial calculations and many other applications. Here are some easy steps to multiply decimals:

• Write down the numbers to be multiplied.
• Ignore the decimal points and multiply as if they are whole numbers.
• Count the total number of decimal places in both numbers.
• Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 3.

For the older problem:

• The numbers to multiply are 0.08 and 1,485.
• Firstly, multiply 8 by 1,485 (ignoring the decimal): \[ 8 \times 1,485 = 11,880 \]
• Since there are two decimal places in 0.08, we place the decimal two places from the right in the product 11,880.
• Thus, the final result is 118.80, meaning Cherise deposited $118.80 into her retirement account.

By understanding these simple steps, multiplying decimals in any problem becomes more manageable and less intimidating.