How do you solve Discount problems?

As an expert in the field of mathematics and economics, I often deal with various types of problems, including those involving discounts. When it comes to solving discount problems, there's a systematic approach one can follow to ensure accuracy and efficiency. Here's a detailed step-by-step guide on how to approach such problems:

### Step 1: Understanding the Problem
Firstly, it's crucial to understand the problem thoroughly. This involves identifying the original price of the item, the discount rate, and what you're being asked to find - whether it's the discount amount, the sale price, or both.

### Step 2: Identifying the Original Price
The original price is the amount you start with before any discounts are applied. This is usually given in the problem statement.

### Step 3: Determining the Discount Rate
The discount rate is typically given as a percentage. It represents the proportion of the original price that will be deducted as the discount.

### Step 4: Calculating the Discount Amount
To find the discount amount, you multiply the original price by the discount rate (expressed as a decimal). This step is crucial because it gives you the exact amount that will be subtracted from the original price.

### Step 5: Converting the Discount Rate to Decimal
Before you can multiply the original price by the discount rate, you need to convert the percentage to a decimal. This is done by dividing the percentage by 100.

### Step 6: Applying the Discount
Once you have the discount amount, you subtract it from the original price to find the sale price. This is the final price that the customer pays after the discount has been applied.

### Step 7: Checking the Calculations
It's always a good practice to double-check your work to ensure that there are no errors. This can be done by verifying that the sale price, when added to the discount amount, equals the original price.

### Example Problem
Let's consider an example to illustrate the process:


1. Original Price (OP): $100

2. Discount Rate (DR): 20%

Now, let's solve for the discount amount and the sale price:

1. Convert the discount rate to a decimal: \( DR = \frac{20}{100} = 0.20 \)
2. Calculate the discount amount: \( Discount = OP \times DR = $100 \times 0.20 = $20 \)
3. Determine the sale price: \( Sale Price = OP - Discount = $100 - $20 = $80 \)

### Common Pitfalls
- Misreading the Problem: It's easy to mix up the original price and the sale price if you're not careful.
- Incorrect Rate Conversion: Failing to convert the percentage to a decimal can lead to incorrect calculations.
- Subtracting in the Wrong Order: The discount must be subtracted from the original price, not the other way around.

### Conclusion
Solving discount problems is a straightforward process once you understand the basic principles and follow the steps methodically. It's a common type of problem in various fields, from retail to finance, and mastering it can be quite beneficial.

Procedure:The rate is usually given as a percent.To find the discount, multiply the rate by the original price.To find the sale price, subtract the discount from original price.