To solve this problem, let's break down the steps clearly and logically:
1. Identify the weights of the books:
- Each math book weighs 3.2 pounds.
- Each workbook weighs 0.8 pounds.
2. Determine the constraint on the total weight:
- The total weight of the box cannot exceed 50 pounds. Therefore, the total weight must be less than or equal to 50 pounds.
3. Formulate the inequality:
- Let [tex]\( x \)[/tex] represent the number of math books.
- Let [tex]\( y \)[/tex] represent the number of workbooks.
4. Express the total weight of the books in terms of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
- Each math book contributes 3.2 pounds, thus [tex]\( 3.2x \)[/tex] represents the total weight of the math books.
- Each workbook contributes 0.8 pounds, thus [tex]\( 0.8y \)[/tex] represents the total weight of the workbooks.
5. Combine these expressions to form the total weight:
[tex]\[ 3.2x + 0.8y \][/tex]
6. Set up the inequality to reflect the maximum weight constraint:
- The total weight [tex]\( 3.2x + 0.8y \)[/tex] should be less than or equal to 50 pounds.
So, the inequality that represents the maximum number of each type of book that can be shipped in a single box is:
[tex]\[ 3.2x + 0.8y \leq 50 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{3.2x + 0.8y \leq 50} \][/tex]
