Question 1119632
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A contractor who does not meet the deadline on the construction of a building is fined $40,000 per day for each of the first ten days of extra time, and for each additional day thereafter the fine is increased by $8,000. If the contractor is fined $1,008,000, by how many extra days was the construction delayed?
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{{{1008000-400000}}}

{{{608000}}}

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The increase after first ten days is ambiguous.  Could be a sequence.
<pre>
ADDITIONAL DAYS       FINE
1                     48000
2                     54000
3                     62000
4                     70000
5                     78000
6                     86000     ------398000
7                     94000
8                    102000     -------594000
9                    110000
</pre>



The extra days, some unknown n, which lead up to fines of 608000 dollars.


Sum from 48000 to 8000(n-1) is  $608000.


{{{(n/2)(48000+48000+(n-1)*8000)=608000}}}------summation formula;

Algebra steps lead to ,...
...
{{{8n^2+88n-1216=0}}}
{{{n^2+11n-152=0}}}
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{{{highlight_green((n-8)(n+19)=0)}}}



The solution looks like {{{highlight_green(n=8)}}} days extra after the first ten.