The average temperature for Monday, Tuesday, Wednesday and Thursday is 60 degrees. The average for Tuesday, Wednesday, Thursday and Friday is 63 degrees. If the ratio of the temperatures on Monday and Friday is 21 : 25, what is the temperature on Friday?

Introduction / Context:
This question is about averages of temperatures over overlapping sets of days and uses a ratio relation between two particular days. It tests your ability to set up equations from average information and then use a simple ratio condition to solve for the unknown temperature on Friday.

Given Data / Assumptions:
- Average temperature for Monday, Tuesday, Wednesday and Thursday = 60 degrees. - Average temperature for Tuesday, Wednesday, Thursday and Friday = 63 degrees. - Let the temperatures on Monday, Tuesday, Wednesday, Thursday and Friday be M, T, W, Th and F respectively. - Ratio of temperatures on Monday and Friday = 21 : 25. - We need to find the value of F.

Concept / Approach:
Average temperature over four days equals the sum of the temperatures of those four days divided by 4. We set up two equations based on the two averages. Then we use the ratio M : F = 21 : 25 to express one temperature in terms of the other. Solving these equations together gives the temperature on Friday. The key step is subtracting one average equation from the other to eliminate T, W and Th and obtain a direct relation between M and F.

Step-by-Step Solution:
Step 1: From the first average, we have: (M + T + W + Th) / 4 = 60. Step 2: Multiply both sides by 4: M + T + W + Th = 240. (Equation 1) Step 3: From the second average, we have: (T + W + Th + F) / 4 = 63. Step 4: Multiply both sides by 4: T + W + Th + F = 252. (Equation 2) Step 5: Subtract Equation 1 from Equation 2: (T + W + Th + F) - (M + T + W + Th) = 252 - 240. Step 6: Simplify: F - M = 12. (Relation 1) Step 7: From the ratio M : F = 21 : 25, we can write: M / F = 21 / 25, so M = (21 / 25) * F. Step 8: Substitute M into Relation 1: F - (21 / 25) * F = 12. Step 9: Factor F: F * (1 - 21 / 25) = 12. Step 10: Compute the bracket: 1 - 21 / 25 = 4 / 25. Step 11: So F * (4 / 25) = 12. Step 12: Multiply both sides by 25 / 4: F = 12 * (25 / 4) = 3 * 25 = 75. Step 13: Therefore, the temperature on Friday is 75 degrees.

Verification / Alternative check:
From F = 75, we get M using the ratio M : F = 21 : 25. So M = (21 / 25) * 75 = 63. Check Equation 1: M + T + W + Th = 240. Equation 2: T + W + Th + F = 252. Subtracting gives F - M = 12, which is 75 - 63 = 12. This matches our relation, confirming the consistency of the value F = 75 degrees.

Why Other Options Are Wrong:
Option A (70°): Would give F - M less than 12 if we retain the ratio 21 : 25. Option B (73°): Does not satisfy both the ratio and the average equations simultaneously. Option D (78°): Also fails when checked against the system of equations derived from the averages. Option E (69°): Too low to maintain the ratio and the 63 degree average together.

Common Pitfalls:
Some learners mistakenly try to average the two given averages directly or ignore the ratio condition completely. Others may confuse which days are in each group and incorrectly set up the equations. The key is to write the equations carefully, eliminate the common terms by subtraction, and then apply the ratio properly to connect Monday and Friday temperatures.

Final Answer:
The temperature on Friday is 75 degrees.