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?
The Correct Answer and Explanation is :
To solve the problem regarding Mr. Ishimoto’s order of math books and workbooks, we need to set up an inequality based on the given information. Let’s denote:
- ( x ) as the number of math books
- ( y ) as the number of workbooks
We know the following:
- Each math book weighs 3.2 pounds.
- Each workbook weighs 0.8 pounds.
- The total weight of the box cannot exceed 50 pounds.
The total weight of the math books and workbooks can be expressed mathematically as:
[
3.2x + 0.8y
]
To ensure the total weight does not exceed 50 pounds, we can formulate the inequality:
[
3.2x + 0.8y \leq 50
]
Explanation of the Inequality:
- Understanding the Variables:
- The variables ( x ) and ( y ) represent the quantities of math books and workbooks, respectively. The weights assigned to each variable reflect the contribution of each book type to the overall weight of the box.
- Weight Contributions:
- The term ( 3.2x ) indicates the total weight contributed by the math books. If Mr. Ishimoto orders ( x ) math books, the total weight for those books will be ( 3.2 ) pounds multiplied by ( x ).
- The term ( 0.8y ) indicates the total weight contributed by the workbooks. If ( y ) workbooks are ordered, their total weight will be ( 0.8 ) pounds multiplied by ( y ).
- Setting the Constraint:
- The inequality ( 3.2x + 0.8y \leq 50 ) clearly states that the combined weight of both types of books must remain at or below the threshold of 50 pounds. This inequality is crucial for ensuring that Mr. Ishimoto adheres to the shipping limitations.
- Graphical Interpretation:
- If plotted on a graph, this inequality would represent a region below and including the line ( 3.2x + 0.8y = 50 ). The intercepts can be calculated to find the maximum number of books that can be shipped, ensuring a practical approach to ordering the books.
This inequality allows Mr. Ishimoto to determine the feasible combinations of math books and workbooks that fit within the shipping weight limit, facilitating efficient ordering for his class.