The average temperature on Friday, Saturday and Sunday was 26∘ and on Saturday, Sunday and Monday it was 24∘. If on Monday it was exactly 25∘. Then what was the temperature on Friday?
31∘
Understanding the Problem
We need to find the temperature on Friday. We are given the average temperature for three days (Friday, Saturday, Sunday) and the average temperature for another three days (Saturday, Sunday, Monday). We also know the exact temperature on Monday.
Calculating Friday's Temperature
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Let the temperatures be represented by variables: $F$ (Friday), $Sa$ (Saturday), $Su$ (Sunday), and $M$ (Monday).
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Write the equations based on the given averages:
- Average (Fri, Sat, Sun): $\frac{F + Sa + Su}{3} = 26^\circ$
- Average (Sat, Sun, Mon): $\frac{Sa + Su + M}{3} = 24^\circ$
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Calculate the total sum of temperatures for each period:
- Sum (Fri, Sat, Sun): $F + Sa + Su = 26 \times 3 = 78^\circ$
- Sum (Sat, Sun, Mon): $Sa + Su + M = 24 \times 3 = 72^\circ$
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Use the given temperature for Monday ($M = 25^\circ$):
- Substitute $M$ into the second sum: $Sa + Su + 25^\circ = 72^\circ$
- Find the sum of Saturday and Sunday temperatures: $Sa + Su = 72^\circ - 25^\circ = 47^\circ$
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Substitute the sum of Saturday and Sunday temperatures ($Sa + Su = 47^\circ$) into the first sum equation:
- $F + 47^\circ = 78^\circ$
- Solve for Friday's temperature: $F = 78^\circ - 47^\circ = 31^\circ$
Therefore, the temperature on Friday was $31^\circ$.
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Important Questions from Average
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