Question

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?

3.2x + 0.8y < 50
3.2x + 0.8y ≤ 50
0.8x + 3.2y < 50
0.8x + 3.2y ≤ 50

Answer 1

The correct inequality is **3.2x + 0.8y ≤ 50**.

The total weight of the box of books is 3.2x + 0.8y. This inequality represents the fact that the total weight of the box of books cannot be more than 50 pounds. The less than or equal to sign (≤) is used because the box of books cannot weigh exactly 50 pounds. If it weighed exactly 50 pounds, then it would be over 50 pounds if even one book were added.

The other inequalities are incorrect because they use the less than sign (<). If the inequality was 3.2x + 0.8y < 50, then it would be possible for the box of books to weigh 49 pounds, which is less than 50 pounds. However, this would violate the condition that the total weight cannot be more than 50 pounds.

Therefore, the correct inequality is 3.2x + 0.8y ≤ 50.