Problem 76 - Elementary Algebra

Question

The regular price of an elliptical trainer is \(\$ 899.99\). It is marked down \(18 \%\). The sales tax is \(7.4 \%\). Find the final cost of the elliptical trainer including tax. Round to the nearest hundredth.

Step-by-Step Solution

Answer

Final cost is = 746.49

Step 1: Calculate the Discount Amount

First, find the discount amount by multiplying the regular price by the discount rate. Discount Amount = Regular Price × Discount Rate = 899.99 × 0.18

Step 2: Subtract the Discount from the Regular Price

Next, subtract the discount amount from the regular price to get the sale price. Sale Price = Regular Price - Discount Amount = 899.99 - (899.99 × 0.18)

Step 3: Calculate the Sales Tax

To find the sales tax, multiply the sale price by the tax rate. Sales Tax = Sale Price × Tax Rate = Sale Price × 0.074

Step 4: Add Sales Tax to the Sale Price

Finally, add the sales tax to the sale price to get the final cost. Final Cost = Sale Price + Sales Tax = Sale Price + (Sale Price × 0.074)

Step 5: Round to the Nearest Hundredth

Round the final cost to the nearest hundredth for the final answer.

Key Concepts

percentage calculations

Understanding percentage calculations is crucial when working with discounts and sales tax. A percentage represents a part of a whole and is expressed as a number out of 100.
For example, in this exercise, we have an 18% discount on the elliptical trainer. This means 18 out of every 100 parts of the regular price is deducted as a discount.
To convert a percentage to a decimal, simply divide by 100. So, 18% becomes 0.18.
When you multiply the original price by this decimal, you determine the discount amount.
This fundamental skill is used not only for discounts but also for calculating sales tax, increases, and decreases in various contexts.

sales tax

Sales tax is an additional percentage that you pay on the sale price of an item. It is important to know how to calculate this tax to find the total cost of a purchase.
In the given exercise, the 7.4% sales tax is applied after the discount price is determined. To calculate sales tax, follow these steps:

• First, determine the sale price by subtracting any discounts from the regular price.
• Next, multiply the sale price by the tax rate (converted to a decimal).
• So, for a 7.4% tax, you multiply by 0.074.

This will give you the amount of sales tax you must add to the sale price. Combining these provides the total cost including tax, ensuring you pay the correct amount.

discounts

Discounts are reductions applied to the original price of an item, making it cheaper.
The discount in the exercise is 18%, which means you save 18% of the original price.
Here's how you calculate the discount step-by-step:

• First, convert the discount percentage to a decimal by dividing by 100.
• Then, multiply the original price by this decimal to find the discount amount.
• Finally, subtract the discount amount from the original price to find the sale price.

Applying these steps helps understand how much you save and what the adjusted sale price is after the discount. This knowledge aids informed purchasing decisions and budget management.