Creating System of Linear equations  TOPIC_SOLVED

Linear spaces and subspaces, linear transformations, bases, etc.

Creating System of Linear equations

Postby johnny23o on Tue Aug 10, 2010 12:04 am

a movie theater charges $9.00 for adults and $7.00 for children. On a day when 325 people purchased tickets, the total receipts were $2675. How many adults tickets were sold? How many children tickets were sold? Create a system of linear equations and solve it using matrices.

I am really lost here please help
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Re: Creating System of Linear equations

Postby Martingale on Tue Aug 10, 2010 2:40 am

johnny23o wrote:a movie theater charges $9.00 for adults and $7.00 for children. On a day when 325 people purchased tickets, the total receipts were $2675. How many adults tickets were sold? How many children tickets were sold? Create a system of linear equations and solve it using matrices.

I am really lost here please help


Let X=#adult tickets
Let Y=#children tickets

now make two liner equations
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Re: Creating System of Linear equations

Postby johnny23o on Tue Aug 10, 2010 1:20 pm

Let x= $9.00
let y= $7.00

9x+7y-325z=2675

would this work?
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Re: Creating System of Linear equations

Postby Martingale on Tue Aug 10, 2010 1:55 pm

johnny23o wrote:Let x= $9.00
let y= $7.00

9x+7y-325z=2675

would this work?


no...you are letting x and y equal costs...let them equal the number of adult and children respectively. you should get two equations not one.
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Postby stapel_eliz on Tue Aug 10, 2010 10:37 pm

johnny23o wrote:Let x= $9.00
let y= $7.00

9x+7y-325z=2675

would this work?

To learn the basic method for setting up this sort of exercise, try here. :wink:
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Re: Creating System of Linear equations  TOPIC_SOLVED

Postby Jaroslaw Jackiw on Mon Sep 13, 2010 10:49 pm

Your problem states that people attended the theater that day, grossing , at per ticket per adult ()and per ticket per child (). This means that times , the number of adults, plus times , the number of children, produced , and that the total number of adults, , plus children, , was . This is your system of linear equations:



You mentioned that you needed to use matrices to solve the problem. Then you will need to convert your system of linear equations to matrix form, as follows:



This will produce a matrix equation of the form for:



such that:



Given and , you need to find , the inverse matrix of , if it exists, to solve the equation. Using elementary row operations on , the augmented matrix of , allows you to obtain :



So that:



Since for:


then:



Therefore, adults and children attended the theater that day.
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