# Math Help - Applied Matrix's and simultaneous equations

1. ## Applied Matrix's and simultaneous equations

I'm really new to this forum so I'm hoping some of you guys can really help me understand some of these concepts and stuff I have =/ I want to learn what I can from you guys and hopefully I can help others also

I've got a question I'm a little stumped on involving matrix's and I'm pretty sure some kind of simultaneous equation and I need to be able to set it out right but maybe bouncing a few idea's off will be able to get me in a right direction

anywhoo question:

People tend to agree public transport is an effecitive way to travel. Public transport combination passes are marketed and sold:

'pass a' cost $12 a week and includes 5 bus rides 2 ferry rides and 3 tram rides 'pass b' costs$20 a week and includes 10 bus rides 5 ferry rides and 5 tram rides

'pass c' costs $15 a week and includes 8 bus rides 4 ferry rides and 3 tram rides in one particular week the number of bus rides sold = 966 the number of ferry rides sold = 467 and the number of tram rides sold = 462 would the turnover made from selling passes exceed$2000? validate the response with your knowledge on matrix's.

Lemme know if I'm on right track here please

a - 5 - 2 - 3 >12
b - 10 - 5 - 5 >20
c - 8 - 4 - 3 > 15

5 2 3 | 12
10 5 5 | 20
8 4 3 | 15

1 0 0 | 3
0 1 0 | -3
0 0 1 | 1

but it's tripping me cos they're paying me (-3) for ferry rides????? I think I'm missing something major and going about it the wrong way... halp?

oh fiddlesticks! I'm not university, sorry I searched matrix's and went to the forum that had most answers, if admin could move topic it'd be much appreciated...

or not, I'm still not university though :P

People tend to agree public transport is an effecitive way to travel. Public transport combination passes are marketed and sold:

'pass a' cost $12 a week and includes 5 bus rides 2 ferry rides and 3 tram rides 'pass b' costs$20 a week and includes 10 bus rides 5 ferry rides and 5 tram rides

'pass c' costs $15 a week and includes 8 bus rides 4 ferry rides and 3 tram rides in one particular week the number of bus rides sold = 966 the number of ferry rides sold = 467 and the number of tram rides sold = 462 would the turnover made from selling passes exceed$2000? validate the response with your knowledge on matrix's.

Let a, b and c denote the sales of the three pass types. Then

Code:
5a+10b+8c=966     //train rides sold
2a+5b+4c=467      //ferry rides sold
3a+5b+3c=462      //tram rides sold
are the equations to be solved.

CB

3. Originally Posted by CaptainBlack
Let a, b and c denote the sales of the three pass types. Then

Code:
5a+10b+8c=966     //train rides sold
2a+5b+4c=467      //ferry rides sold
3a+5b+3c=462      //tram rides sold
are the equations to be solved.

CB
sooo...
32 x 12
51 x 20 = $1959 so doesn't exceed$2000
37 x 15

Okay now I have an answer I know how to get... cool
now I understand how we get that in simultaneous equation land

how can I apply my knowledge of matrix's and use them to solve it now??

4. By the way, the plural of "matrix" is "matrices", not "matrix's". A plural never has an apostrophe.