Used books cost $2.25 each. Which expression represents the total number of books that can be purchased for $10?
[tex]$\left\lfloor\frac{10}{2.25}\right\rfloor$[/tex]
[tex]$\left\lceil\frac{10}{2.25}\right\rceil$[/tex]
[tex]$\frac{10}{\lceil 2.25\rceil}$[/tex]
[tex]$\frac{10}{\lfloor 2.25\rfloor}$[/tex]
Answer (2)
Divide the total money by the cost per book: 2.25 10 .
Apply the floor function to round down to the nearest whole number since you can only buy whole books: ⌊ 2.25 10 ⌋ .
The expression representing the total number of books that can be purchased is ⌊ 2.25 10 ⌋ .
Therefore, the answer is ⌊ 2.25 10 ⌋ .
Explanation
Understanding the Problem We are given that each used book costs $2.25 and we have $10 to spend. We want to find the expression that represents the total number of books we can purchase.
Calculating the Maximum Number of Books To find the maximum number of books we can buy, we need to divide the total amount of money we have by the cost of each book. This gives us 2.25 10 .
Applying the Floor Function Since we can only buy whole books, we need to round down the result to the nearest whole number. This is because we can't buy a fraction of a book. The floor function, denoted by ⌊ x ⌋ , gives the largest integer less than or equal to x . Therefore, we need to use the floor function to round down the result.
Final Expression Thus, the expression that represents the total number of books we can purchase is ⌊ 2.25 10 ⌋ .
Calculating the Number of Books Let's calculate the value to understand better. 2.25 10 = 4.444... . Applying the floor function, we get ⌊ 4.444... ⌋ = 4 . So, we can buy 4 books.
Examples
Imagine you are at a bookstore with $10 and each book costs $2.25. You want to know how many books you can buy without spending more than you have. This problem helps you determine the maximum number of books you can purchase. Understanding how to use the floor function in this context can help you make informed purchasing decisions in various real-life scenarios, such as buying groceries or planning a budget. This ensures you don't exceed your budget and get the most out of your money.
To find out how many used books you can purchase for $10 at $2.25 each, divide $10 by $2.25 and apply the floor function to round down to a whole number. The correct expression representing the total number of books that can be purchased is ⌊ 2.25 10 ⌋ . Therefore, you can buy 4 books with your budget.
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