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

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 $ 0.75p $.
- **Store B** offers a flat $180 reduction from the original price. So, the sale price at Store B is $ p - 180 $.

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

\[
0.75p = p - 180
\]

This matches the first option:  
**$ 0.75p = p - 180 $**

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

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Here are 5 questions that expand on the situation:
1. How can you solve the equation $ 0.75p = 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.

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. Which equation models this situation?

Learn how to model and solve a problem comparing two different types of discounts: a 25% off sale and a $180 reduction. This algebra problem teaches students how to set up and solve equations based on percentage and fixed discounts, suitable for Grades 8-10.

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