A piece of ribbon 4 yards long is used to make bows, each bow requiring 15 inches of ribbon. What is the maximum number of bows that can be made from this ribbon?

Introduction / Context:
This problem is a straightforward unit conversion and division question. A ribbon of a certain length is cut into equal pieces to make bows, and we must determine how many pieces of the required length can be obtained. The key idea is to convert all lengths into the same unit and then perform integer division to find how many complete pieces fit into the total length.

Given Data / Assumptions:

- Total length of ribbon is 4 yards. - Each bow requires 15 inches of ribbon. - We can only count complete bows, not partial ones. - Standard conversion is 1 yard = 36 inches.

Concept / Approach:
Since the bow length is given in inches, it is convenient to convert the total ribbon length from yards to inches. Once we know the total length in inches, we divide by 15 to find how many bows of 15 inches can be formed. The quotient tells us the number of complete bows, and any remainder represents leftover ribbon that is too short for another bow.

Step-by-Step Solution:
Step 1: Convert 4 yards to inches using the conversion 1 yard = 36 inches. Step 2: Compute 4 * 36 = 144 inches. So the ribbon is 144 inches long. Step 3: Each bow requires 15 inches of ribbon. Step 4: Divide the total length by the length per bow: 144 ÷ 15. Step 5: Compute the quotient: 15 * 9 = 135 and 15 * 10 = 150 which exceeds 144. So the maximum number of full bows is 9. Step 6: The remainder is 144 − 135 = 9 inches, which is not enough for one more 15 inch bow.

Verification / Alternative check:
We can also reason in reverse. If we make 9 bows, they use 9 * 15 = 135 inches of ribbon. This is less than or equal to the total 144 inches. Attempting 10 bows would require 10 * 15 = 150 inches, which is more than 144 and therefore impossible. This confirms that 9 is the maximum number of bows that can be made.

Why Other Options Are Wrong:
Option A (8) is too small because we can clearly fit 9 bows into 144 inches. Options C (10) and D (11) require more ribbon than is available, so those counts are not feasible. Only 9 matches both the capacity and the maximal requirement.

Common Pitfalls:
Some learners forget to convert yards to inches correctly and may assume a wrong conversion factor. Others may mistakenly round up after division, which would correspond to making a partial bow. In such problems we must always take the integer part of the division since only complete bows count.

Final Answer:
The maximum number of bows that can be made is 9, which matches option B.