DVDs were in a sale bin at Discount-Mart. All DVDs in the bin cost less than $5.50. What was the most a customer could have possibly paid for a DVD in the bin? Enter your answer as dollars and cents. Use the variable p to enter an inequality that represents the possible price of a DVD in the bin in dollars.
Answer (2)
A customer could pay a maximum of 5.49 f or a D V D in t h es a l e bina t D i sco u n t − M a r t , an d t h e in e q u a l i t yre p rese n t in g t h e p oss ib l e p r i ce i s p < 5.50.
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The maximum possible price for a DVD is a value just below $5.50.
In dollars and cents, this maximum price is $5.49.
The inequality representing the possible price p is expressed as p < 5.50 .
Therefore, the maximum price is $5.49 and the inequality is p < 5.50 .
Explanation
Understanding the Problem We are given that all DVDs in the bin cost less than $5.50. We need to find the maximum possible price a customer could have paid, expressed in dollars and cents, and also represent the possible prices as an inequality using the variable p.
Determining the Maximum Price Since the DVDs cost less than $5.50, the maximum price would be infinitesimally smaller than $5.50. However, since we need to express the answer in dollars and cents, we need to find the largest value less than $5.50 that can be expressed in dollars and cents. This value is $5.49.
Expressing the Inequality To express the possible prices of a DVD using the variable p, we can write the inequality as p < 5.50, which means the price p is less than $5.50.
Examples
Imagine you're at a school fair where all game tickets cost less than $2. If you want to figure out the most you might spend on a single ticket, you'd use a similar approach. Since the tickets are less than $2, the most you could pay is $1.99. This kind of problem helps you understand limits and maximum values in everyday situations, like budgeting or shopping within constraints.
