The average temperature of a city for the first sixteen days of January is 22°C, and the average temperature for the last sixteen days of the same month is 26°C. If the average temperature for the entire month is 24°C, what is the temperature on the sixteenth day?

Question

Accepted Answer

Let the temperature on the 16th day be x°C.

Let S1 be the sum of temperatures for the first 16 days, and S2 be the sum for the last 16 days.

Given:
- Average for first 16 days = 22°C ⇒ S1 = 16 × 22 = 352
- Average for last 16 days = 26°C ⇒ S2 = 16 × 26 = 416
- January has 31 days. Average for 31 days = 24°C ⇒ Total sum = 31 × 24 = 744

Notice that the 16th day is included in both the first 16 days and the last 16 days. So, if we add S1 and S2, the temperature of the 16th day is counted twice.

So,
S1 + S2 = (sum of temperatures for days 1 to 16) + (sum for days 16 to 31)
= (sum for days 1 to 15) + (temperature on 16th day) + (temperature on 16th day) + (sum for days 17 to 31)
= (sum for days 1 to 15) + (sum for days 17 to 31) + 2 × (temperature on 16th day)
= (sum for all 31 days) + (temperature on 16th day)

Therefore,
S1 + S2 = (sum for all 31 days) + (temperature on 16th day)
352 + 416 = 744 + x
768 = 744 + x
x = 768 - 744 = 24

So, the temperature on the 16th day is 24°C.

Answer

Answer

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