explanation pls.??

\(40x= (x-4)(80)\)

\(-40x=-320\)

\(x= 7.8\)

x must be at least 8 to bring the average age up over 40.

Hope this helps.

Regards

if (x-4)80=40x, then (x-4)80 keeps average equal to 40 and there are the rest 4 buildings aged 2 years less than others .
Therefore, the value X ( integer as it is building number )decides the range of the number of buildings.
Thank you,
It helps immensely .
regards

I still don't get how the equation was set up

I set up the equation differently:

The average age of any set of buildings would be defined as: [total age in years of all the buildings] / [# of buildings]

In this case, we have 4 buildings built 2 years ago (4*2 = 8 years), and we can pretend that the rest of the buildings are 80 years old to solve for the extreme case. Let B be the REST of the buildings. So:

[total age in years of all the buildings] = 8 + 80B.

The total number of buildings will be 4 + B.

Solve for the inequality:

[8+80B]/[B+4] > 40
You'll get
B>3.8

You have to go back and add the remaining 4 buildings back in...

B>3.8+4 --> B>7.8

So, B > 7.8, which makes the answer choices C D and E

Let, total buildings = x

4 of them are 2 years old, so a total of 4*2 = 8 years old

remaining (x - 4) buildings are at most 80 years old. So in total of (x - 4)*80 years old.

So,
(8 + (x - 4)*80) / x = 40
=> x = 7.8 = 8 (As we have to consider the average greater than 40)

At least 8 buildings are there. So, we can consider the numbers that are greater than or equal to 8.

Ans: C, D, E

Carcass, as per your equation, x equates to 8 and not 7.8. There is some dissonance that needs to be cleared.

Thanks in advance for your clarification!

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