Mr. Ishimoto ordered x new math books and y new workbooks for his class. The total weight of the box of books cannot be more than 50 pounds. If each math book weighs 3.2 pounds and each workbook weighs 0.8 pounds, which inequality represents the maximum number of each type of book that can be shipped in a single box?
A. 3.2x + 0.8y < 50
B. 3.2x + 0.8y ≤ 50
C. 0.8x + 3.2y < 50
D. 0.8x + 3.2y ≤ 50
The Correct Answer and Explanation is:
The correct answer is B. 3.2x + 0.8y ≤ 50.
Explanation:
This problem involves determining how many math books and workbooks can be shipped in a single box without exceeding a weight limit. Here’s how we can break it down:
- Let x represent the number of math books.
- Let y represent the number of workbooks.
- The weight of each math book is given as 3.2 pounds.
- The weight of each workbook is given as 0.8 pounds.
The total weight of the books in the box is the sum of the weight of the math books and the weight of the workbooks. Thus, the total weight of the books can be expressed as:
[
\text{Total weight} = 3.2x + 0.8y
]
Where:
- (3.2x) represents the weight of (x) math books.
- (0.8y) represents the weight of (y) workbooks.
The problem states that the total weight cannot exceed 50 pounds. Therefore, the total weight must be less than or equal to 50 pounds. This condition is mathematically represented by the inequality:
[
3.2x + 0.8y \leq 50
]
This inequality tells us that the combined weight of the math books and the workbooks must be 50 pounds or less, which is consistent with the problem’s requirements.
Why the other options are incorrect:
- Option A: 3.2x + 0.8y < 50
This inequality uses a strict less-than symbol (<), which means the total weight must be less than 50 pounds but cannot equal 50. However, the problem allows the weight to be exactly 50 pounds, so this is not correct. - Option C: 0.8x + 3.2y < 50
In this option, the roles of the math books and workbooks are reversed, and it incorrectly places the weight of the math books as 0.8x and the weight of the workbooks as 3.2y. This is not how the weights were given in the problem. - Option D: 0.8x + 3.2y ≤ 50
Similar to Option C, this incorrectly swaps the weights of the math books and workbooks. It would suggest that workbooks weigh more than math books, which contradicts the given information.
Thus, the correct inequality is B: 3.2x + 0.8y ≤ 50, as it accurately represents the relationship between the number of books and the total weight constraint.