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A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $182,600? The number of tickets for sale at $26 should be.

A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $182,600? The number of tickets for sale at $26 should be.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $182,600? The number of tickets for sale at $26 should be D00 20 ODO F4 esc
Transcribed Image Text:A 6000-seat theater has tickets for sale at $26 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $182,600? The number of tickets for sale at $26 should be D00 20 ODO F4 esc
Expert Solution
Step 1

Given that total number of seats is 6000.

We have to find the number of tickets for sale at $26.

Let x tickets are sold at the sale $26.

Then 6000-x tickets will be sold at sale $40.

Therefore, total revenue is given by

Revenue=26x+406000−x

Sine, total revenue is given by $182,600.

Hence, 26x+406000−x=$182,600

⇒26x+240,000−40x=182,600⇒26x−40x=182,600−240,000⇒−14x=−57,400⇒x=−57,400−14⇒x=4,100

Hence, x=4,100.

 

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