Math Is Fun Forum

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Matrix help me...........

One travels company flies three kinds of airplanes: the Airbus 100, the Airbus 200, and the Airbus 300. Each plane is outfitted with tourist, economy, and first-class seats. The number of each kind of seat in the three types of planes is shown below. The second chart lists the number of reservations for its July flight to France. How many of each kind of plane should the company fly to fill all the seats?

                          Airbus A        Airbus B            Airbus C
     Tourist                 50              75                  40
     Economy              30              45                  25
     First Class            32              50                  30

Category                 Number of reservations
Tourist Class                305
Economy Class             185
First Class                    206

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Letter, number, arts and science
of living kinds, both are the eyes.

justlookingforthemoment

Moderator

Registered: 2005-05-26

Posts: 2,161

Re: Matrix help me...........

This problem is similar to the one you posted earlier about capsules and drugs. It can be solved in the same way as mathsyperson showed.

Here are your three simultaneous equations:

50a + 75b +  40c = 305 [1]
30a + 45b + 25c = 185 [2]
32a + 50b + 30 = 206 [3]

You could simplify if you wanted:
[1] simplifies 10a + 15b + 8c = 61
[2] simplifies 6a + 9b + 5c = 37
[3] simplifies 16a + 25b + 15c = 103

(where a, b and c are the respective airbuses.)

Combine equations and eliminate the variable 'c':

3*[2] - [3] --> 2a + 2b = 8 [4]
5*[1] - 8*[2] --> 2a + 3b = 9 [5]

So, like before, we now have two equations.

[5] - [4] --> b = 1

If you substitute b into either equation [4] or [5], you will be able to find a. Then, using the results for a and b, substitute them into equation [1], [2] or [3] to find c.

So, the airline company should fly three 'A' airbuses, one 'B' airbus, and two 'c' airbuses.

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Re: Matrix help me...........

Thanks a lot

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Letter, number, arts and science
of living kinds, both are the eyes.

FarazAhmad

Guest

Re: Matrix help me...........

even though i was looking solution in matrix form but this helped me alot.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Matrix help me...........

Hi FarazAhmad;

This is what those simultaneous set of linear equations look like in matrix form of Ax = b:

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If it ain't broke, fix it until it is.
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