Question 1068133
Let X be the number of nights in hotel A and Y the number of nights in hotel B.
{{{X+Y<8}}} - Total number of nights
{{{125X+80Y<800}}} - Total cost of the hotels
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*[illustration gd8.JPG].
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The inequality is really only valid for the black dots not the entire region. 
You can't stay at a hotel for 2.2 nights you can only stay at a hotel for an integer number of nights.