Question

The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.​

Answer 1

Area of 7th hall = 37 m^2

Explanation:

Total area of 7 halls = 7*55 = 385

Total area of 6 halls = 6*58 = 348

Area of 7th hall = 385-348 = 37 m^2

Answer 2

The area of the seventh hall = 37m²

Explanation:

for 6 halls

Mean area of 6 halls = 58m²

`Mean\ area = (sum\ of\ areas)/(Number\ of\ halls) \\58\ =\ (sum\ of\ areas)/(6) \\sum\ of\ areas\ of\ 6\ halls\ = 58\ *\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348`

Let the area of the 7th hall be x

The sum of the areas of 7 halls = 348 + x - - - - - - (1)

`Mean = (sum\ of\ the\ areas\ of\ 7\ halls)/(7) \\55 = (sum\ of\ the\ areas\ of\ 7\ halls)/(7) \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ *\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)`

notice that equation (1) = equation (2)

348 + x = 385

x = 385 - 348 = 37m²

Therefore, the area of the seventh hall = 37m²