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Chapter 8: Problem 49

An exercise machine with an original price of \(\$ 860\) is on sale at \(12 \%\) off. a. What is the discount amount? b. What is the exercise machine's sale price?

Short Answer

Expert verified
a. The discount amount is \$103.2. b. The sale price of the exercise machine is \$756.8.

Step by step solution

01

Determine the discount amount

First we need to find the discount amount. This can be found by multiplying the original price by the discount rate (which needs to be in decimal form).\n So, \(\$860 \times 0.12 = \$103.2\) Thus, the discount amount is \$103.2
02

Find the sale price

The sale price can be found by subtracting the discount amount from the original price. So, we have, \(\$860 - \$103.2 = \$756.8\). Therefore, the sale price of the exercise machine is \$756.8.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Discount Calculation
When you hear about discounts in a shopping context, it's all about saving money! Calculating a discount is the first step towards knowing how much you'll save on an item. To find the discount amount, you multiply the original price by the discount rate.
If an exercise machine costs \(\\(860\) and is on sale for \(12\%\) off, the discount rate as a decimal is \(0.12\).
  • Convert the percentage to a decimal by dividing by \(100\) (i.e., \(12\% = 0.12\)).
  • Multiply the original price by the discount rate: \(\\)860 \times 0.12 = \\(103.2\).
Therefore, \(\\)103.2\) is the discount amount you'll subtract from the original price.
Figuring Out the Sale Price Calculation
Once you have the discount amount, the next step is determining the sale price of the item. The sale price is what you'll actually pay once the discount is applied. Start by subtracting the discount from the original price.
  • The original price here is \(\\(860\).
  • The discount amount you calculated is \(\\)103.2\).
  • Subtract \(\\(103.2\) from \(\\)860\) to get the sale price.
Thus, the sale price is \(\$756.8\).
Simple subtraction helps conclude your sale price calculation.
Enhancing Skills in Mathematical Problem Solving
Solving problems like this involves a series of mathematical operations, bringing together skills in percentages and basic arithmetic. It's essential to understand each step to solve similar problems in the future.
  • Step-by-step process: Breaking a problem into small, manageable steps can make complex problems easier to handle.
  • Conversions: Learn to confidently convert percentages to decimals and vice versa.
  • Practice: Continue practicing with different values to become proficient at quick calculations.
The more problems you solve, the deeper your understanding will become. This helps build a solid foundation for more challenging real-life math scenarios!

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Most popular questions from this chapter

Use this advice from most financial advisers to solve Exercises 11-12. \- Spend no more than \(28 \%\) of your gross monthly income for your mortgage payment. \- Spend no more than \(36 \%\) of your gross monthly income for your total monthly debt. Round all computations to the nearest dollar. Suppose that your gross annual income is \(\$ 36,000\). a. What is the maximum amount you should spend each month on a mortgage payment? b. What is the maximum amount you should spend each month for total credit obligations? c. If your monthly mortgage payment is \(70 \%\) of the maximum you can afford, what is the maximum amount you should spend each month for all other debt?

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