The average temperature for Monday, Tuesday, Wednesday and Thursday is 48 degrees. The average temperature for Tuesday, Wednesday, Thursday and Friday is 52 degrees. If the temperature on Monday is 42 degrees, what is the temperature on Friday?

Introduction / Context:
This temperature problem uses overlapping averages over consecutive days of the week. You know the average from Monday to Thursday, and from Tuesday to Friday, and you also know the temperature on Monday. From this information, you must compute the temperature on Friday. It is a standard example of using sums from averages for consecutive groups.

Given Data / Assumptions:
- Let the temperatures on Monday, Tuesday, Wednesday, Thursday and Friday be M, T, W, Th and F respectively.
- Average for Monday to Thursday = 48 degrees.
- Average for Tuesday to Friday = 52 degrees.
- Temperature on Monday M = 42 degrees.
- We need to find the temperature on Friday F.

Concept / Approach:
The average of four days is the sum of their temperatures divided by 4. So each given average can be turned into an equation for the sum of those four days. Subtracting these equations allows you to isolate the difference between Friday and Monday temperatures. Since Monday's temperature is known, you can then solve for Friday's temperature directly.

Step-by-Step Solution:
Step 1: From the first average, (M + T + W + Th) / 4 = 48.Step 2: Multiply by 4: M + T + W + Th = 4 * 48 = 192.Step 3: From the second average, (T + W + Th + F) / 4 = 52.Step 4: Multiply by 4: T + W + Th + F = 4 * 52 = 208.Step 5: Subtract the first sum from the second: (T + W + Th + F) - (M + T + W + Th) = 208 - 192.Step 6: This simplifies to F - M = 16.Step 7: Given M = 42, substitute to get F - 42 = 16.Step 8: Therefore F = 42 + 16 = 58 degrees.

Verification / Alternative Check:
If Friday's temperature is 58, the sum Tuesday to Friday is T + W + Th + 58 = 208. Since M + T + W + Th = 192 and M = 42, we have T + W + Th = 150. Then T + W + Th + 58 = 150 + 58 = 208, matching the second sum. So the averages and individual values are consistent, confirming F = 58.

Why Other Options Are Wrong:
Values like 56, 52 or 50 do not satisfy the equation F - M = 16 when M = 42. Substituting any of these into the sum equations would not produce the correct second average of 52 degrees. Only 58 degrees satisfies all conditions of the problem.

Common Pitfalls:
Some students incorrectly average 48 and 52 directly or forget to multiply by 4 when finding the sums. Others make mistakes during subtraction of the equations. To avoid such errors, always convert averages to sums first, then subtract carefully to isolate the unknown temperature.

Final Answer:
The temperature on Friday is 58 degrees.