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 .
- Store B offers a flat $180 reduction from the original price. So, the sale price at Store B is .
Since Brittany concludes that the sale prices at both stores are the same, we can equate these two expressions:
This matches the first option:
Would you like to go into further details or have any questions?
Here are 5 questions that expand on the situation:
- How can you solve the equation ?
- What is the original price of the computer based on the equation?
- How would the situation change if Store B reduced the price by a different amount, say $200?
- What would the discount percentage be in Store B if the sale price was identical but given as a percentage off instead of $180?
- 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
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