# Real life applications of simultaneous equations

Discussion in 'Mathematics' started by hammie, Feb 22, 2012.

1. ### hammieLead commenter

a bit harsh don't you think?
the rest of your post will be quite helpful to someone whose school doesn't use a good core text

No.

3. ### mleisam

My students have always actually enjoyed the mobile phone contract example. The best one I did was a lesson where I told the students I wanted an iPhone and gave them information about different real contracts and told them I needed their help to decide which one to go for. They really enjoyed it and came up with all sorts of reasons I hadn't thought of for which company to choose. They worked out which one was cheaper overall and discussed things like how long to stay with each company and when they become cheaper but also mentioned things like, "Do any of them come with insurance for your new phone?" So I don't think that is an overused real-life application. I think it is one that the students can really relate to. Much better than oranges and bananas! There is a video on what used to be teacherstv (but they are now on TES somewhere) about mobile phones which I have also used.

neddyfonk likes this.
4. ### lizziec

Linear programming in D1 textbooks or revision guides usually give slightly more realistic examples and require solution of simultaneous equations. Whether you also teach the rest of linear programming as an extension is up to you!
Hope this helps...

Liz

5. ### afterdarkLead commenter

I disagree, shopping comparisons are real life.
A restaurant bill is another example.
An accountant has to itemise 3 hand written bills that do not show any sub totalling.
Given that the prices remain the same between bills find the individual item costs.
3 Coffees 3 set Meals 3 Desserts = 24 quid
4 Coffees 3 set Meals 2 Desserts = 23.25
5 Coffees 4 set Meals 1 Desserts = 24.50
You didn't say 2 X 2 simultaneous equations did you?
Unless, of course, by 'real life' you mean the very limited life experiences of teenagers who have never left their local estate.
Why don't you say in 'real life' there are much more complicated problems?
You could even show then how to reduce the 3 equations above from 3 unknowns to 2 equations in 2 unknowns.
These are just the linear first order...
I find the argument 'that is not real life' rather fatuous.

6. ### PaulDGOccasional commenter

Radar collision avoidance systems & the reverse - guided missile systems solve simultaneous equations in real time (i.e. transformed to the time domain). The "solution" is the impact point.

Possibly a bit beyond most Yr 9s though.

Yes, the trouble is, they're not ready for "real life"..

7. ### ian60New commenter

I remember watching an OU vid many years ago in B/W where 3 bearded maths types went into a pub and ordered some drinks.
Fast forward...
They went to the bar but ordered a different number of the same drinks.
Repeat
The question was then, how much does a pint of Guiness cost.
However, the crafty sods, had thrown a spanner in the works because the cost of a pint was (something like) 37p, but the cost of a half was 19p and not
18 1/2 p
Thus making it a very unstable system of equations.
My! How those OU blokes laughed when they explained the issue.
(I really miss OU maths lecturers with strange beards)

8. ### MasterMaths

With the 5 nations going on ... why not mess around with the points scored for tries/conversions/penalties?
EDIT - what decade is it!?!?! I meant 6 nations!

9. ### halelucy

And that was Live on Mars, that was.... I am getting nostalgic as well!

10. ### AnonymousNew commenter

Do people score tries nowadays?

(apart from England today of course)

11. ### PiranhaStar commenter

I have seen loads of questions along the lines of the ones mentioned, but it would be nice to have some which are genuine uses in real life. In practice, we know how much things cost or what a try is worth - we don't calculate such figures from totals. I think that the phone tariff thing is really just a linear equation - make the formula from company A equal to that from B, solve and then do the inequality. I know that we run into simultaneous equations in A-level Applied Maths, but does anybody know a genuine real life application that KS3 and 4 students can relate to? (I am quite happy to teach it without, but it would be nice to have one.) The Linear Programming idea sounds good once we have graphs of inequalities.

12. ### PaulDGOccasional commenter

From my experience, there are very few "real world" applications of anything KS3/4 students can relate to.

This isn't to do them down, but when you look at the number of things they have to cope with in their lives to do with growing up, the opposite (or same) sex, clothes & teen culture, what's going on at home and then they have to cope with 5 or six different subjects being thrown at them every day, there just isn't the space left in most of their heads to try to make connections in depth.

When kids ask "what is this for?" they're generally asking for two reasons - the first is "is this on the exam", so they know if they even have to bother paying any sort of attention and the second is the hope that you'll digress into what it's for so they can sit back for 10 minutes.

Kids who actually want to know what a technique can be used for are pretty rare - the "genuine" ones will already have an application in mind because it chimes with their interests and they will either not ask or, if they do ask, are seeking confirmation.

13. ### RickkNew commenter

I appreciate this is an old post but I have the same issue. The apples and pears problems are contrived, you wouldn't stand in a supermarket working out simultaneous equations. On the other hand the maths has to be accessible so you can't start with anything too complicated.

So I'm looking at doing a starter video about Air traffic control, that apparently uses simultaneous equations, then going in to the usual maths lesson type questions. The video / real-life content would be to capture interest rather than be the main part of the lesson.

Any thoughts?

14. ### VoltamathsNew commenter

Air traffic control’s use of simultaneous equations to avoid collision of planes can make for a great start. Budding chemists, will like the problem of mixing 10% concentrated solution of HCl and 60 % concentrated solution of HCl to make 10 litres of 50 % solution of HCl.
You will get two simultaneous equations x+y=10 and 0.1x+0.6y=(0.5 X 10) Ie x+6y=50

You can adapt this to make it about alcohol concentration in cocktail, Alcohol concentration to say within drinking limits for driving etc.

15. ### armandine2Established commenter

I was going to post something like this - before thread started - simple electric circuit analysis typically ends up with a simeq. First you need to explain Kirchhoff current law and voltage distribution law (both more straightforward than they sound).

16. ### RickkNew commenter

Thank you for the Replies - just seen them as the email went in to my Junk box

I've since found that air traffic controllers use an equation for the safe height for the flight of a plane dependant on air pressure - and it's straightforward for relative beginners to equations

17. ### bluesam33New commenter

The trick might be to instead look for applications of matrix inversion, the two being essentially the same (anything practical you do with a matrix inverse of A is likely going to involve multiplying it by some vector v, at which point you're just solving the simultaneous equation Ax = v for x). Given that, any application you find for inverse matrices is also an application for solving simultaneous equations. For a starting point: if you've got a video game, and you've got a character that's moving around, you're very often going to have to convert pixel coordinates on the screen to positions relative to the character, and vice versa. It's generally fairly easy to get the conversion matrix in one direction (there'll also be an offset between the origin points, but that just adds some constant terms to your simultaneous equations). That is: you get some simultaneous equations in the x and y coordinates on the screen which give you the coordinates relative to the character (call them u and v, for example). That lets you get equations of the form ax + by + c = u and dx + ey + d = v, which let you convert from screen coordinates to character coordinates by just substituting in x and y. If you want to go the other way (and don't know what an inverse matrix is), you then need to substitute in your values for u and v, then solve the simultaneous equations for x and y.
More generally, any time you've got one coordinate system defined in terms of another and need to convert between them, you've got some simultaneous equations that let you go in one direction by substitution, but require you to solve those simultaneous equations to go the other way: OS grid reference to lat-long is (if we take a local approximation to latitude/longitude to keep things linear) is essentially identical, for example.

18. ### neddyfonkLead commenter

Many moons ago I subscribed to New Scientist and spent hours trying to solve the puzzles. Then I bought a book on Operational Research which had a fairly short program written in BASIC which did the donkey work of solving many simultaneous equations. It also had a program for the Newton-Ralphson method of calculating square roots - which was nice.