AllExperts > Word Problems 
Search      
Word Problems
Volunteer
Answers to thousands of questions
 Home · More Word Problems Questions · Answer Library  · Encyclopedia ·
More Word Problems Answers
Question Library

Ask a question about Word Problems
Volunteer
Experts of the Month
Expert Login

Awards

About Us
Tell friends
Link to Us
Disclaimer

 
 
 
 
About Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience
Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

 
   

You are here:  Experts > Science > Math for Kids > Word Problems > Matrix Word Problem

Word Problems - Matrix Word Problem


Expert: Abe Mantell - 8/12/2009

Question
I'm trying to convert the following problem into a Matrix to solve by calculator (the solving part is not the problem). Can you help?

A basketball fieldhouse seats 15,000. Courtside seats cost $12, endzone seats cost $9, and balcony seats cost $6. The total revenue for a sellout is $80,000. If half the courtside seats, half the balcony seats, and all the endzone seats are sold, then the total revenue is $50,000. How many of each type of seats are there?

Your help would be greatly appreciated.

Answer
Hello Ann,


Let x=# of courtside seats sold,
let y=# of endzone seats sold, and
let z=# of balcony seats sold.

Thus, we get the following equations:
1. x + y + z = 15,000 (the total # of tickets sold)
2. 12x + 9y + 6z = 80,000 (total revenue)
3. 12(x/2) + 9y + 6(z/2) = 50,000 (the last criteria you gave)

Thus all we need to do is solve the system:
x+y+z=15000
12x+9y+6z=80000
6x+9y+3z=50000

The trouble is the solution does not make sense!
Aside from fractional values, x turns out to be negative!!!
{x = -25000/9, y = 20000/9, z = 140000/9}

Are you sure the problem is correctly stated?

TTYL, Abe


Add to this Answer   Ask a Question


 
User Agreement | Privacy Policy | Kids' Privacy Policy | Help
Copyright  © 2008 About, Inc. AllExperts, AllExperts.com, and About.com are registered trademarks of About, Inc. All rights reserved.