Math Problem Statement

Given: amount of discount = $9.90, net price = $20.10. Question: what is the discount rate in percentage?

Solution

The discount rate in percentage is calculated using the formula:

Discount Rate=(Discount AmountOriginal Price)×100\text{Discount Rate} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100

Given:

  • Discount Amount = $9.90
  • Net Price = $20.10

Step 1: Find the Original Price

Original Price=Net Price+Discount Amount\text{Original Price} = \text{Net Price} + \text{Discount Amount} =20.10+9.90=30.00= 20.10 + 9.90 = 30.00

Step 2: Compute the Discount Rate

Discount Rate=(9.9030.00)×100\text{Discount Rate} = \left( \frac{9.90}{30.00} \right) \times 100

=0.33×100= 0.33 \times 100

=33%= 33\%

Final Answer:

The discount rate is 33%.

Would you like further details or a breakdown?

Here are five related questions you might find interesting:

  1. If the discount rate were increased to 40%, what would the new net price be?
  2. How do you calculate the selling price if a 33% discount is applied to any price?
  3. If tax is applied after the discount, how does it affect the final price?
  4. What is the relationship between markup and discount percentage?
  5. How would you determine the discount amount if only the original price and discount rate were given?

Tip: Always double-check percentage calculations by working backward to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Percentage Calculation
Basic Arithmetic

Formulas

Discount Rate = (Discount Amount / Original Price) * 100
Original Price = Net Price + Discount Amount

Theorems

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Suitable Grade Level

Grades 7-9