Problem 141 - Elementary Algebra

Question

Erys bought a treadmill on sale at \(35 \%\) off. The original price was \(\$ 949.95\) (round to the nearest cent.)

Step-by-Step Solution

Answer

The sale price is \(617.47\).

Step 1 - Calculate the Discount Amount

First, determine the discount amount by multiplying the original price by the discount percentage. The original price is \(\$949.95\) and the discount is \(35\%\). Therefore, the discount amount is \(\text{Discount Amount} = 949.95 \times 0.35\).

Step 2 - Perform the Multiplication

Now perform the multiplication: \(949.95 \times 0.35 = 332.4825\).

Step 3 - Round the Discount Amount

Round the discount amount to the nearest cent, which is \(332.48\).

Step 4 - Calculate the Sale Price

Subtract the discount amount from the original price: \(949.95 - 332.48\). \(\text{Sale Price} = 617.47\).

Step 5 - Round the Sale Price

Round the sale price to the nearest cent (if necessary). In this case, \(617.47\) is already rounded to the nearest cent.

Key Concepts

percentage discount

Percentage discount is a way to determine how much less you'll pay for an item. It's usually given as a percent, like 35%. To find the discount amount, you multiply the original price by the discount percentage (written as a decimal).
Here, the original price is $949.95 and the discount is 35%.
This means you'll pay 35% less.
We can calculate it using:
\( \text{Discount Amount} = \text{Original Price} \times \text{Discount Percentage} \).
Remember, convert the percent to a decimal by dividing by 100.
So, 35% becomes 0.35.
This simple multiplication helps find the exact amount saved.

multiplication

Multiplication is a core arithmetic operation used in many calculations, including discounts.
For Erys's treadmill discount, we multiply the original price by the decimal form of the discount percent.
In this case, that's \(949.95 \times 0.35 \).
This step gives the amount saved due to the discount.
Use a calculator or do it by hand to find the value.
Here, \(949.95 \times 0.35 = 332.4825 \). This number represents the total discount amount before rounding.
Multiplication makes it easy to see big savings quickly.

rounding to nearest cent

When dealing with money, it's important to round to the nearest cent.
Cents are the two digits after the decimal point in dollars.
After calculating the discount amount as 332.4825, we need to round it.
Look at the third digit after the decimal point (in this case, 2).
If it's 5 or more, round up the second digit.
If it's less than 5, keep the second digit as it is.
So, 332.4825 rounds to 332.48.
This makes the discount accurate for financial transactions.

subtraction

To find the final sale price after the discount, we use subtraction.
Subtract the rounded discount amount from the original price.
The calculation is: \(949.95 - 332.48 \).
This gives us \(617.47 \).
This number is the price Erys will pay for the treadmill after applying the discount.
By subtracting the discount from the original price, we get the final amount owed.
This step ensures you know exactly how much you save and what the new price is.