In terms of the variable x, how many total days are there in a time period of x weeks and x additional days?

Introduction / Context:
This is a basic algebra and calendar question that combines the concept of weeks and days. It tests whether you can express a verbal time description, namely x weeks and x days, as a single algebraic expression in terms of the total number of days. Such conversions between units are very common in time and work, calendar and speed problems.

Given Data / Assumptions:
- The duration is x weeks and x days.
- One week consists of exactly 7 days.
- We must write the total duration in days as a simplified algebraic expression in x.
- x is assumed to be a positive integer for typical aptitude questions, although the algebra works for any real x.

Concept / Approach:
To convert weeks to days, we multiply the number of weeks by 7. Then we add the extra days given. Because both quantities depend on x, we will end up with an expression like 7x plus x. Finally, we simplify this expression to a single term by combining like terms. This is a straightforward application of distributive and additive properties in algebra.

Step-by-Step Solution:
Step 1: Start with the expression x weeks and x days.Step 2: Convert x weeks into days. Since 1 week = 7 days, x weeks = 7 * x days = 7x days.Step 3: The total number of days is then 7x days from the weeks plus x additional days.Step 4: Write this as an algebraic sum: total days = 7x + x.Step 5: Combine like terms: 7x + x = 8x.Step 6: Therefore, the total number of days in x weeks and x days is 8x days.

Verification / Alternative check:
To verify the expression, choose a specific value for x. For example, let x = 2. Then the duration is 2 weeks and 2 days. Two weeks is 14 days and plus 2 days gives 16 days. Our algebraic formula 8x gives 8 * 2 = 16 days, which matches the direct calculation. Trying a few different values such as x = 3 or x = 5 will give the same agreement, confirming that 8x is correct.

Why Other Options Are Wrong:
The option 7x ignores the extra x days and counts only the weeks. The option 14x is what you would get if you incorrectly multiplied both the weeks and the days by 7. The option 7 gives a fixed number of days independent of x, which cannot be correct because the time period clearly grows as x increases. The expression x + 7 treats the contributions additively but does not scale the weeks properly and is not dimensionally consistent for large x values.

Common Pitfalls:
Learners sometimes forget to convert weeks into days at all, or they mistakenly think 1 week equals 10 days. Another common error is failing to combine like terms and leaving the answer as 7x + x instead of simplifying to 8x. Always remember basic unit conversions and algebraic simplification rules to avoid these mistakes.

Final Answer:
The total number of days in x weeks and x days is 8x days.