Question

A concert hall has 8,000 seats and two categories of ticket prices, $29 and $34. Assume that all seats in each category can be sold.
Concert
2
8,000
$255,000
1
8,000
$271,000
Tickets sold
Return required
3
8,000
$235,000
a. How many tickets of each category should be sold to bring in each of the returns indicated in the table?
$29 Tickets
$34 Tickets
Concert 1

Answer 1

Using a system of equations, it is found that:

• For a profit of $255,000, 3400 tickets of $29 and 4600 tickets of $34 must be sold.
• For a profit of $271,000, 200 tickets of $29 and 7800 tickets of $34 must be sold.
• For a profit of $235,000, 7400 tickets of $29 and 600 tickets of $34 must be sold.

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The variables of the system are:

• x, which is the number of $29 tickets sold.
• y, which is the number of $34 tickets sold.

Total of 8,000 seats, all can be sold, thus:

$x + y = 8000 \rightarrow x = 8000 - y$

--------------------

For a profit of $255,000, we have that:

$29x + 34y = 255000$

$29(8000 - y) + 34y = 255000$

$5y = 23000$

$y = \frac{23000}{5}$

$y = 4600$

$x = 8000 - 4600 = 3400$

For a profit of $255,000, 3400 tickets of $29 and 4600 tickets of $34 must be sold.

--------------------

For a profit of $271,000, we have that:

$29x + 34y = 271000$

$29(8000 - y) + 34y = 271000$

$5y = 39000$

$y = \frac{39000}{5}$

$y = 7800$

$x = 8000 - 7800= 200$

For a profit of $271,000, 200 tickets of $29 and 7800 tickets of $34 must be sold.

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For a profit of $235,000, we have that:

$29x + 34y = 235000$

$29(8000 - y) + 34y = 235000$

$5y = 3000$

$y = \frac{3000}{5}$

$y = 600$

$x = 8000 - 600 = 7400$

For a profit of $235,000, 7400 tickets of $29 and 600 tickets of $34 must be sold.

A similar problem is given at brainly.com/question/22826010