Used books cost $2.25 each. Which expression represents the total number of books that can be purchased for $10?
A. $\left\lfloor\frac{10}{2.25}\right\rfloor$
B. $\left\lceil\frac{10}{2.25}\right\rceil$
C. $\frac{10}{\lceil 2.25\rceil}$
D. $\frac{10}{\lfloor 2.25\rfloor}$
Answer (1)
Divide the total amount available by the cost of each book: 2.25 10 .
Round down to the nearest integer using the floor function: ⌊ 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 used books cost $2.25 each, and we want to find the expression that represents the total number of books that can be purchased for $10. Since we can only buy whole books, we need to find the largest whole number of books we can buy with $10. This involves dividing the total amount of money by the cost per book and then rounding down to the nearest whole number.
Dividing Total Money by Cost per Book To find the maximum number of books we can buy, we divide the total amount of money, $10, by the cost of each book, $2.25. This gives us 2.25 10 .
Applying the Floor Function Since we can only buy whole books, we need to round down to the nearest whole number. The floor function, denoted by ⌊ x ⌋ , gives the largest integer less than or equal to x . Therefore, the expression representing the total number of books that can be purchased is ⌊ 2.25 10 ⌋ .
Final Answer The expression that represents the total number of books that can be purchased for $10 is ⌊ 2.25 10 ⌋ .
Examples
Imagine you have a $10 bill and you're at a used bookstore where each book costs $2.25. The expression ⌊ 2.25 10 ⌋ tells you exactly how many books you can walk out with. This concept is useful in everyday budgeting, like figuring out how many items you can buy with a certain amount of money, considering the individual cost of each item. For instance, if you have $20 and each snack costs $3.50, ⌊ 3.50 20 ⌋ will tell you how many snacks you can purchase.
