The drama club is selling tickets to their play to raise money for the show's expenses. each student ticket sells for $5.50 and each adult ticket sells for $7.50. the auditorium can hold a maximum of 140 people. the drama club must make at least $910 from ticket sales to cover the show's costs. if 66 student tickets were sold, determine the minimum number of adult tickets that the drama club must sell in order to meet the show's expenses. if there are no possible solutions, submit an empty answer.

We want to find an inequality that represents the given situation.

The inequality is:

74 ≥ x ≥ 73

The given information is:

Now we know that 66 student tickets were sold, so the profit for this is:

66*$5.50 = $363

Then now the drama club must make at least:

$910 - $363 = $547

And the number of places left is 140 - 66 =  74.

Now let's define x as the number of adult tickets that they must sell, we will have that the profit for these x tickets is:

x*$7.50

And this must be at least $547, then we have:

x*$7.50 ≥ $547

Solving this for x, we get:

x ≥ $547/$7.50 = 72.9

This could be rounded to the next whole number, so we get:

x ≥ 73

And we also have the restriction that a maximum of 74 tickets can be sold, so the inequality will be:

74 ≥ x ≥ 73

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Step-by-step explanation:

We are going to assume that the show is sold out.  If 66 student tickets were sold, we only have 74 adult tickets to sell.  Based on that information, we then have to use an inequality to find out if the number of adult tickets we have to sell to meet our money requirements is more than the amount of seating we have left after 66 seats were taken by students.  Our inequality looks like this:

5.50(66) + 7.50(a) ≥ 910 and

363 + 7.50a ≥ 910 and

7.50a ≥ 547 so

a ≥ 73

In order to meet our money requirement, we have to sell 73 adult tickets.  Since we have 74 seats left, we are good.

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.