Each window covering can span 15 identical windows in a row. How many such window coverings are needed to span a total of 50 windows?

Introduction:
This question involves simple division and the idea of rounding up to the next whole number. We want to cover a certain number of windows using window coverings, each of which can cover only a fixed number of windows. Since the number of coverings must be a whole number, any fraction means one more full covering is required.

Given Data / Assumptions:
- Each window covering is long enough to cover 15 windows. - There are 50 windows that need to be spanned. - We assume partial coverings are not allowed; each covering is a complete unit. - We must find the minimum number of coverings needed to span all 50 windows.

Concept / Approach:
The basic concept is to divide the total number of windows by the number of windows each covering can span. If the result is an integer, that is the answer. If the result is not an integer, we must round up to the next whole number, because even a small remainder of uncovered windows requires an additional full covering.

Step-by-Step Solution:
Step 1: Total number of windows to be covered = 50. Step 2: Capacity of one window covering = 15 windows. Step 3: Compute 50 / 15. Step 4: 15 * 3 = 45 and 15 * 4 = 60, so 50 / 15 is between 3 and 4. Step 5: Numerically, 50 / 15 is approximately 3.33. Step 6: Since we cannot use a fraction of a window covering, we must round 3.33 up to the next whole number. Step 7: Therefore, the number of window coverings required is 4.

Verification / Alternative Check:
If we use 3 coverings, they will span 3 * 15 = 45 windows, which leaves 5 windows uncovered. That is not acceptable. If we use 4 coverings, they span 4 * 15 = 60 windows, which is more than enough to cover 50 windows. Thus 4 coverings are sufficient and also the minimum number required.

Why Other Options Are Wrong:
Option 3: Only covers 45 windows, leaving some windows uncovered. Options 5, 6 and 7: All of these provide more coverings than required, so they are not the minimum number of coverings.

Common Pitfalls:
One common mistake is to take the integer part of 50 / 15 as the answer, which would give 3. However, in real life and in such problems, even a small uncovered part requires one additional full unit. The correct method is to round up, not to round down, whenever there is any remainder.

Final Answer:
The number of window coverings needed is 4.