Problem 67 - Elementary Algebra

Question

The original price of a computer is \(\$ 899\). If it is marked down \(23 \%\), find the sale price.

Step-by-Step Solution

Answer

The sale price is \$692.23\.

Step 1 - Convert the percentage to a decimal

First, convert the markdown percentage to a decimal. To do this, divide the percentage by 100. So, \(23\text{\%} = \frac{23}{100} = 0.23\).

Step 2 - Calculate the discount amount

Next, calculate the discount amount by multiplying the original price by the decimal. So, \(\text{Discount Amount} = 899 \times 0.23 = 206.77\).

Step 3 - Subtract the discount from the original price

Finally, subtract the discount amount from the original price to find the sale price. So, \(\text{Sale Price} = 899 - 206.77 = 692.23\).

Key Concepts

Percentage to Decimal Conversion

Converting a percentage to a decimal is the first crucial step in many calculations, such as finding discounts. This process is straightforward: simply divide the percentage value by 100. For instance, in our exercise, we need to convert a 23% markdown to a decimal. To achieve this, we perform the division:

• 23 divided by 100 equals 0.23.

By understanding this conversion, you can quickly move from a percentage to a decimal form, making various mathematical operations more manageable. Remember, the rule is always to divide by 100.

Multiplying Decimals

With the decimal value at hand, the next step is to calculate the discount amount. This involves multiplying the original price by the decimal value. Multiplying decimals can seem challenging, but it's straightforward once you understand the steps:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both numbers being multiplied.
3. Place the decimal point in the product (result) so that it has the same number of decimal places as the total from step 2.

For our example:

• We multiply 899 by 0.23:
  1. 899 (whole number) times 23 (whole number without the decimal) equals 20,677.
  2. The original numbers had a total of two decimal places (none in 899 but two in 0.23).
  3. So, we place the decimal point two places from the right in 20,677, giving us 206.77.

This product, 206.77, is the discount amount.

Subtracting Decimals

The final step is to find the sale price by subtracting the discount amount from the original price. Subtracting decimals follows similar rules to subtracting whole numbers, with the added step of aligning the decimal points.

1. Write the numbers in a vertical column, making sure the decimal points are lined up.
2. Subtract as if they were whole numbers, beginning from the rightmost digit.
3. Keep the decimal point directly below the other decimal points in the equation.

In our example:

• We start with 899 (original price) minus 206.77 (discount amount).

Aligning the decimal points directly:

• 9.00 - 6.77 breaks down to:
  1. Borrowing across the zeros:
  2. 8.00 - 0.77 equals 7.23.

Thus, the final sale price is 692.23. By mastering these simple steps - converting percentages to decimals, multiplying decimals, and subtracting decimals - you can quickly and accurately find the sale price during discounts.