The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees. The average for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees, what was the temperature on Friday?

Introduction / Context:
This problem is another example of overlapping averages used to find an unknown value. It involves daily temperatures across two overlapping groups of four days. The first group includes Monday and the second group includes Friday. Using the difference between the two group sums and the known Monday temperature, we can determine Friday's temperature.

Given Data / Assumptions:

• Average temperature for Monday, Tuesday, Wednesday, Thursday = 48 degrees.
• Average temperature for Tuesday, Wednesday, Thursday, Friday = 46 degrees.
• Temperature on Monday = 42 degrees.
• We must find the temperature on Friday.

Concept / Approach:
The approach is to convert averages to total sums over four days each, then subtract to find the difference between Friday and Monday. The key relationship is: (sum of second group) - (sum of first group) = Friday temperature minus Monday temperature, because the middle three days are common to both groups and cancel out.

Step-by-Step Solution:
Let the temperatures on Monday to Friday be M, T, W, Th, F.Average for Monday to Thursday is 48, so M + T + W + Th = 48 * 4 = 192.Average for Tuesday to Friday is 46, so T + W + Th + F = 46 * 4 = 184.Subtract the first equation from the second: (T + W + Th + F) - (M + T + W + Th) = 184 - 192.This simplifies to F - M = -8.Given M (Monday) = 42 degrees, so F - 42 = -8.Hence F = 42 - 8 = 34 degrees.Therefore, the temperature on Friday was 34 degrees.

Verification / Alternative check:
Check the sums explicitly. If Monday is 42 and Friday is 34, then F - M = 34 - 42 = -8, matching our equation. Let the sum of Tuesday, Wednesday and Thursday be S. Then M + S = 192 gives S = 192 - 42 = 150. Also, S + F must equal 184, and 150 + 34 = 184. Both conditions are satisfied, so the answer is consistent.

Why Other Options Are Wrong:
If you choose 36, 38 or 40 degrees for Friday, the difference F - M would not equal -8 and you would not obtain the given averages. Each incorrect value results in inconsistent sums for the two groups of days. Only Friday = 34 degrees keeps both averages correct.

Common Pitfalls:
Some exam takers attempt to average 48 and 46 directly or forget that the middle three days cancel when subtracting. Others accidentally compute M - F instead of F - M, which flips the sign and leads to a wrong answer. Carefully writing the equations and subtracting them in the correct order avoids these errors.

Final Answer:
The temperature on Friday was 34 degrees.