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 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.

facundo3141592 facundo3141592 · Answer 2 · 2021-10-05T12:56:48+02:00

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

The inequality is:

74 ≥ x ≥ 73

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The given information is:

Each student ticket sells for $5.50
Each adult ticket sells for $7.50
The auditorium can hold a maximum of 140 people.
The drama club must make at least $910

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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