Problem 16 - Prealgebra

Question

Solve each of these problems using the method developed in this section. A man buys a washing machine that is on sale. The washing machine usually sells for \(\$ 450\) but is on sale at \(20 \%\) off. If the sales tax rate in his state is \(6 \%\), how much is the total bill for the washer?

Step-by-Step Solution

Answer

The total bill for the washer is $381.60.

Step 1: Calculate the Sale Price

First, we need to calculate the sale price of the washing machine after the 20% discount. The discount amount is 20% of the usual price, which is calculated as follows: \\[ \text{Discount} = 0.20 \times 450 = 90.00 \]\The sale price is then the usual price minus the discount amount: \\[ \text{Sale Price} = 450 - 90 = 360 \]

Step 2: Calculate the Sales Tax Amount

Next, we need to find the sales tax on the discounted price. The sales tax rate is 6%, so the tax amount is 6% of the sale price. This is calculated by: \\[ \text{Sales Tax} = 0.06 \times 360 = 21.60 \]

Step 3: Calculate the Total Bill

Finally, add the sales tax amount to the sale price to find the total bill. The calculation is as follows: \\[ \text{Total Bill} = 360 + 21.60 = 381.60 \]

Key Concepts

Discount Calculation

Calculating discounts is a straightforward way to determine how much you'll save on an item. For instance, when a washing machine is offered at a 20% discount, the first step is figuring out the discount amount. You'll use the formula: \[ \text{Discount} = \text{Original Price} \times \frac{\text{Discount Rate}}{100} \]For a washing machine priced at \(450, you'd calculate:\[ \text{Discount} = 450 \times 0.20 = 90 \]The \)90 is what you save because of the discount. Simply subtract this from the original price to get the sale price:\[ \text{Sale Price} = \text{Original Price} - \text{Discount} \]In this case, it's \(450 - \)90, so $360 is what you'd pay before any additional fees, like sales tax, are applied. Remember, the key is understanding that a discount is just a percentage reduction off the original price. This is an essential concept in everyday shopping and helps you become a savvy spender!

Sales Tax Calculation

Once you've identified the discounted price, the next step is to calculate any additional charges, such as sales tax. Sales tax is a percentage added to the sale price of an item based on state laws. Here's the basic formula for calculating it:\[ \text{Sales Tax} = \text{Sale Price} \times \frac{\text{Tax Rate}}{100} \]For the washing machine priced at \(360, if the state tax rate is 6%, calculate it as follows:\[ \text{Sales Tax} = 360 \times 0.06 = 21.60 \]This \)21.60 is then added to the sale price to find out how much you'll actually pay at the register. Understanding sales tax is critical because it affects the final amount you owe. Even after discounts, sales tax ensures that you’re aware of the total actual cost for goods.

Final Pricing Calculation

After calculating both the discount and sales tax, the last step is determining the final price, also known as the total bill. This total cost includes both the discounted price of the item and the sales tax. It's computed with this basic formula:\[ \text{Total Cost} = \text{Sale Price} + \text{Sales Tax} \]For the washing machine, that means:\[ \text{Total Cost} = 360 + 21.60 = 381.60 \]So, the washing machine that originally cost \(450, after deducting the discount and adding the sales tax, results in a total payment of \)381.60. Understanding how to compute the final price is vital not just for budgeting during shopping but also for financial planning. Always remember that discounts don't necessarily reflect the final price until taxes and other fees are applied.