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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.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter3: Math Models
Section3.3: Solve Mixture Applications
Problem 3.58TI: At the movie theater, the total value of tickets sold was $2,612.50. Adult tickets sold for $10 each...
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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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