How many separate window coverings are required to completely span a row of 50 windows, if each single window covering can continuously cover 15 windows in a line?

Introduction / Context:
This question is a basic application of averages and division in a real life style context. We are told that one long window covering can span several windows in a row and we must work out how many such coverings are needed to span all the windows in the line. The core idea is to see how many groups of a fixed size can fit into a total and then recognise that if there is any remainder, we still need one extra covering to complete the span.

Given Data / Assumptions:

• Total number of windows to be covered = 50.
• Each window covering can span 15 windows in a straight line.
• We assume that window coverings cannot be cut or partially used; each covering is used as a whole piece.
• We must find the minimum number of coverings needed so that all 50 windows are covered.

Concept / Approach:
The main concept is simple division with a remainder. To see how many coverings are needed, we divide the total number of windows by the number of windows that one covering can span. If the total is not a perfect multiple, the remainder indicates that we need one additional full covering. Mathematically, this is the ceiling of 50 divided by 15.

Step-by-Step Solution:
Step 1: Write the basic division: number of coverings = 50 / 15. Step 2: Compute 50 / 15 = 3.333..., which means 3 complete groups of 15 windows and some windows left over. Step 3: Each full group of 15 windows uses one covering, so 3 complete groups use 3 coverings. Step 4: Number of windows covered by 3 coverings = 3 * 15 = 45 windows. Step 5: Remaining windows to be covered = 50 - 45 = 5 windows. Step 6: Even though only 5 windows are left, we still need one whole extra covering to span these remaining windows. Step 7: Therefore, the total number of coverings required = 3 + 1 = 4.

Verification / Alternative check:
We can quickly check by multiplying the answer back. If we use 4 coverings with a capacity of 15 windows each, the maximum span is 4 * 15 = 60 windows. Since 60 is more than 50, we definitely have enough length to cover all windows. With only 3 coverings, we would cover at most 45 windows, leaving 5 uncovered, which is not acceptable. Therefore 4 coverings is the smallest number that works.

Why Other Options Are Wrong:
Three coverings (option 3) can cover only 45 windows, so 5 windows remain uncovered. Fifteen coverings or 50 coverings are far more than necessary and do not reflect the capacity of each covering. The option 5 coverings is not minimal because 4 coverings already suffice to cover all 50 windows.

Common Pitfalls:
A common mistake is to take only the integer part of 50 / 15 and answer 3 without thinking about the remainder. Another typical error is to assume that a partially used covering somehow does not count as a full covering. In reality, if you need even part of another covering, you must count that entire piece. Remember that for these types of questions, if there is any remainder after division, you must take the next whole number.

Final Answer:
The number of window coverings required to span all 50 windows is 4.