Math Problem Statement

Two stores sell the same computer for the same original price. Store A advertises that the computer is on sale for 25% off the original price. Store B advertises that it is reducing the computer’s price by $180. When Brittany compares the sale prices of the computer in both stores, she concludes that the sale prices are equal.

Let p represent the computer’s original price.

Which equation models this situation?

Responses

0.75p=p−180 0.75 p equals p minus 180

0.25p=p−180 0.25 p equals p minus 180

0.25(p−180)=p 0.25 left parenthesis p minus 180 right parenthesis equals p

0.75p=p+180 0.75 p equals p plus 180

Solution

To model this situation, let's break it down:

  • Store A offers a 25% discount on the original price, meaning the price after discount is 75% of the original price. So, the sale price at Store A is represented as 0.75p0.75p.
  • Store B offers a flat $180 reduction from the original price. So, the sale price at Store B is p180p - 180.

Since Brittany concludes that the sale prices at both stores are the same, we can equate these two expressions:

0.75p=p1800.75p = p - 180

This matches the first option:
0.75p=p1800.75p = p - 180

Would you like to go into further details or have any questions?


Here are 5 questions that expand on the situation:

  1. How can you solve the equation 0.75p=p1800.75p = p - 180?
  2. What is the original price of the computer based on the equation?
  3. How would the situation change if Store B reduced the price by a different amount, say $200?
  4. What would the discount percentage be in Store B if the sale price was identical but given as a percentage off instead of $180?
  5. How do percentage-based discounts compare to fixed-amount discounts for different original prices?

Tip: When comparing discounts, remember that percentage discounts affect larger original prices more significantly than flat-rate discounts.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Discount Calculation

Formulas

0.75p = p - 180 (for percentage and fixed discounts)

Theorems

Equality of Expressions

Suitable Grade Level

Grades 8-10