Question

Using Matrices to Solve Systems of Equations and show work!!!!

17. Last Monday at 7:30 a.m., an airline flew 89 passengers on a commuter flight from Boston to New York. Some of the passengers paid $120 for their tickets and the rest paid $230 for their tickets. The total cost of all of the tickets was $14,200. How many passengers bought $120 tickets? How many bought $230 tickets?

Answer 1

Where are you stuck?

Answer 2

set up of the systems of equations: for example: 4a + 2b = 12

Answer 3

and matrix part

Answer 4

Nope
let a is a number of passenger paid $120
b is a number of passenger paid $230
Then, a +b =89 ok??

Answer 5

"an airline flew 89 passengers....."
Make sure that you get the concept. If you get it, let me know to step up

Answer 6

there are 2 equations

Answer 7

YYYYYYYYYYYes, Sir!! but you have to get the first one first :)

Answer 8

yes I get it

Answer 9

Now, the second one:
then a*120 is the amount of money of the paid-$120 passengers paid
b*230 is the amount of money of the paid-$230 passenger paid
and 120a + 230b = 14200
get it?

Answer 10

then since we have the 2 equations we can put them in matrices

Answer 11

yes,
I rewrite it:
a + b = 89
120a +230b=14200
now, write it as a matrix

Answer 12

\[\left[\begin{matrix}1&1&89\\120&230&14200\end{matrix}\right]\]

Answer 13

get it?

Answer 14

you don't write 89 and 14200 in the same matrix you write it in a different one. the inverse of matrix A * matrix B

Answer 15

in a 2x1 matrix = 89 and 14,200

Answer 16

oh!! that way!! oooooooook
since I solve it in calculator, I combine them all. But if you have to solve it by that way, it's ok

Answer 17

we write the answer in an ordered pair

Answer 18

you have:
\(\left[\begin{matrix}1&1\\120&230\end{matrix}\right]\)\(\left[\begin{matrix}a\\b\end{matrix}\right]\)=\(\left[\begin{matrix}89\\14200\end{matrix}\right]\)

Answer 19

right?

Answer 20

yes

Answer 21

so, to find the answer, you need inverse of the first matrix, right?

Answer 22

right times B and he has the answers in fractions

Answer 23

Ax = B , then x = \(A^{-1}B\), is it what you want?

Answer 24

yep

Answer 25

ok, do you know how to find inverse of the first matrix?

Answer 26

inverse of this\(\left[\begin{matrix}1&1\\120&230\end{matrix}\right]\)

Answer 27

If you know, try it. When touching matrix, I don't think you can skip any step or rely on others. YOU, have to master it. Try it. I can check.
Since you don't know how to combine all, just take step by step, I think you are new in the field. So, Practice, please.

Answer 28

I am waiting for your reply. If you are not interesting on YOUR problem anymore, we stop here. :)

Answer 29

I think multiply by the matrix 1 0
0 1

Answer 30

I just click the inverse button on my calculator

Answer 31

nope, if you are allowed to use calculator, then use it to find the inverse of it. Do you know how?

Answer 32

1) enter the whole matrix , not 1 0
0 1

Answer 33

what's the whole matrix

Answer 34

\(\left[\begin{matrix}1&1\\120&230\end{matrix}\right]\)

Answer 35

by 1 0
0 1

Answer 36

oh, boy!!
ok, again, not 1 0 /0 1

Answer 37

you enter the second matrix: (89 /14200)

Answer 38

yes I know duh

Answer 39

then hit matrix button to call the first one out,
hit the inverse button, DON'T HIT ENTER YET
hit times button
hit matrix button again to call the second one,
then ENTER,

Answer 40

yep I know how to do it and I got the answer (512/11, 412/11)

Answer 41

What do you get?

Answer 42

Hello! I got the answer (512/11, 412/11)

Answer 43

NOpe, you must have \(\left[\begin{matrix}57\\32\end{matrix}\right]\) that is the right answer

Answer 44

You make mistake at somewhere. let's think !! a, b are passengers, they must be integers, you can't have 1 and a half person, right? so, if the answer is not integers, you are wrong for sure.