Let's break down the problem step-by-step to determine the correct inequality representing the maximum number of each type of book that can be shipped in a single box.
1. Understand the given data:
- Each math book weighs 3.2 pounds.
- Each workbook weighs 0.8 pounds.
- The total weight of the box cannot exceed 50 pounds.
2. Formulate the weight equation:
- Let [tex]\(x\)[/tex] be the number of math books.
- Let [tex]\(y\)[/tex] be the number of workbooks.
- The total weight contributed by the math books in the box is [tex]\(3.2x\)[/tex] (since each math book weighs 3.2 pounds).
- The total weight contributed by the workbooks in the box is [tex]\(0.8y\)[/tex] (since each workbook weighs 0.8 pounds).
- The combined weight of the math books and workbooks in the box is [tex]\(3.2x + 0.8y\)[/tex].
3. Set up the inequality:
- The total weight of all the books in the box must not exceed 50 pounds. Therefore, we can represent this situation with the inequality [tex]\(3.2x + 0.8y \leq 50\)[/tex].
4. Verify the options:
- [tex]\(3.2x + 0.8y < 50\)[/tex]: This option implies that the total weight must be strictly less than 50 pounds, which does not account for the case when the total weight is exactly 50 pounds.
- [tex]\(3.2x + 0.8y \leq 50\)[/tex]: This option accurately represents that the total weight can be up to 50 pounds, but not exceeding it.
- [tex]\(0.8x + 3.2y < 50\)[/tex]: This switches the coefficients for math books and workbooks, which is incorrect.
- [tex]\(0.8x + 3.2y \leq 50\)[/tex]: This option also incorrectly switches the coefficients for math books and workbooks.
Based on the analysis, the correct inequality is:
[tex]\[ 3.2x + 0.8y \leq 50 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{3.2x + 0.8y \leq 50} \][/tex]
