Emily is going to the bookstore. Paperback books cost $3.20 each and hardcover books cost $10.00 each. Which inequality best represents how many paperback books and how many hardcover books Emily can buy without spending more than $65?
A. $5p + 10h \leq 65$
B. $3.50p + 10h \geq 65$
C. $4.50p + 10h = 45$
D. $3.20p + 10h \leq 65$
Answer (1)
The inequality that represents the situation is 3.20 p + 10 h ≤ 65 .
Explanation
Understanding the Problem Let's break down this problem. We need to figure out which inequality correctly represents the situation where Emily buys paperback and hardcover books without spending more than $65 .
Defining Variables Let's use variables to represent the unknowns:
Let p be the number of paperback books Emily buys.
Let h be the number of hardcover books Emily buys.
Expressing the Cost Now, let's express the cost of the books in terms of these variables:
The cost of p paperback books is $3.20 p .
The cost of h hardcover books is $10.00 h .
Formulating the Inequality The total cost of the books is the sum of the cost of paperback books and the cost of hardcover books, which is 3.20 p + 10 h . Since Emily cannot spend more than $65 , the total cost must be less than or equal to $65 . This gives us the inequality: 3.20 p + 10 h ≤ 65
Final Answer Therefore, the inequality that best represents the situation is 3.20 p + 10 h ≤ 65 .
Examples
Imagine you're planning a school event and have a budget of $500 for snacks. If juice boxes cost $2 each and bags of chips cost $3 each, this type of inequality helps you determine how many of each item you can buy without exceeding your budget. For example, if you buy 100 juice boxes, you can then calculate the maximum number of chip bags you can afford. This ensures you stay within your financial limits while providing a variety of snacks for the event.
