The length of a string is 8 feet 9 inches, and it is divided into 3 equal parts. What is the length of each part in inches?

Introduction / Context:
This is a straightforward unit conversion and division problem. A length given in mixed units of feet and inches has to be converted entirely into inches and then divided into three equal parts. The question checks knowledge of simple unit conversion within the imperial system and basic arithmetic operations.

Given Data / Assumptions:

• Total length of the string is 8 feet 9 inches.
• 1 foot equals 12 inches.
• The string is divided into 3 equal parts.
• We need the length of each part expressed in inches.

Concept / Approach:
The approach is to convert the entire length into a single unit, inches. This avoids handling mixed units while dividing. Once we have the total length in inches, we simply divide by 3 to get the length of each equal part. Finally, we compare that result with the options provided.

Step-by-Step Solution:
Step 1: Convert 8 feet into inches. Using 1 foot = 12 inches, 8 feet = 8 * 12 = 96 inches.Step 2: Add the extra 9 inches to this value: 96 + 9 = 105 inches.Step 3: The total length of the string is therefore 105 inches.Step 4: The string is divided into 3 equal parts, so length of each part = 105 / 3 inches.Step 5: Compute 105 / 3 = 35 inches.Step 6: Each equal part of the string is 35 inches long.

Verification / Alternative check:
Multiply the length of one part by 3 to check if we get back the total length: 35 * 3 = 105 inches.Convert 105 inches back into feet and inches: 105 / 12 = 8 feet with remainder 9 inches, because 8 * 12 = 96 and 105 - 96 = 9.Thus, 105 inches corresponds to 8 feet 9 inches, confirming that the conversion and division were carried out correctly.

Why Other Options Are Wrong:
Numbers like 31 or 33 inches, when multiplied by 3, give totals smaller than 105 inches, so they do not reconstruct the original length of the string.Values such as 37 inches or 29 inches, multiplied by 3, give totals greater or less than 105 inches, again failing to match the original length.Only 35 inches when tripled returns exactly the starting length of 8 feet 9 inches.

Common Pitfalls:
A typical mistake is to divide the feet and inches separately without first converting to a common unit, which can lead to fractional feet and inconsistent results.Another error is forgetting that 1 foot equals 12 inches and using an incorrect conversion factor.Rounding is not needed here because the division is exact, so any rounding would be unnecessary and misleading.

Final Answer:
Each part of the string is 35 inches long.