h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It makes no difference how many times people write the answers to the maths problems I'm doing - I can't remember how to do simultaneous equations and I am having a near total meltdown on my economics course over it.

I am back at the point where I'm seriously considering jacking it all in.

again.

my tutor said that I shouldn't sweat the maths stuff - which is ok in an essay question but there are also maths questions. And I want to get them right.

So can anyone recommend a website or a book that can explain just why x should move from here to there...

I really really really don't want any of my friends to start explaining it to me. I have had a bellyfull of well-meaning people trying to do that and it just makes me frustrated, angry and shouty.

Seriously: don't ruin our friendship by trying to explain it. It's not worth the teeth marks.

But a book rec or a revision website rec would be great. (it's the explaining to me aspect of it that is making me not want to put this in ask.)

I'll explain it to you as much as you like, Sho, and I don't care how much you shout.

seriously, I get so amazingly grumpy.

OK since it's you let's give it a go. (even though the notation isn't going to be easy here...)

This is the problem:

If it is reported that the (annualised) yield on a 91-day £100,000 Treasury bill has fallen to 2.5 per cent, calculate the discount at which this bill was sold. Show your answer to two decimal places.

I know that I have to take the difference in the face price of the bill and what I paid for it and make that into a percentage.

We can call that X.

so far then the equation looks like this:

(x / 100,000 - x)

then I multiply that by the annual interest for a 91 day bond

(365/91)

and the answer to that little baby is 2.5 per cent

so the equation is

(x / (100,000 - x)) * (365 / 91) = 2.5

which gives

(x / (100,000 - x)) * 4.010989 = 2.5

Now, apparently, I can rearrange it to give:


0.025*(100000 – x) = 4.010989x

but I don't know how they got there.
I would have put the 2.5 over the 4.01...

of course it would help if I had writen 2.5% as 0.025 and not 2.5



so the equation as I see it is

(x / (100,000 - x)) * 4.010989 = 0.025

and because I have to go out in a minute their explanation looks like this (with my comments in [square brackets]

0.025*(100000 – x) = 4.010989x

[ok I got this far. when you bring something to the other side of the = it changes from division to multiplication and vice versa]

2500 – 0.025x = 4.010989x

[how they jumped from the last to this is a complete mystery:
or they multiplied something by 100,000 for a reason I can't fathom - and makes the rest of it just gobbledegook]

Gathering the x we get
4.010989x + 0.025x = 2500
4.035989x = 2500
x = (2500/4.035989) = 619.42686

I don't know anything about treasury bonds, so I don't know whether your original equation is completely correct, but I can see a problem in it. You've said

(x / (100,000 - x)) * (365 / 91) = 2.5

But it's not equal to 2.5, it is equal to 2.5%. You can write 2.5% as 2.5/100 or as 0.025. So it should be:

(x / (100,000 - x)) * (365 / 91) = 0.025

This isn't actually a simultaneous equation, because simultaneous equations are where you have two equations, with two different variables, or three equations with three variables etc. This is a single equation with two x's in it. The problem is to fiddle around with it until you have only one x on one side of the equal sign, and something you can calculate on the other side.

You can multiply both sides of an equation by anything and it will still be true. So you can multiply both sides of this by (100,000 - x). YOu'll get:

(x / (100,000 - x)) * (365 / 91) * (100,000 - x) = 0.025 * (100,000 - x)

You should be able to see that on the left hand side you are dividing and multiplying by (100,000 - x) so these will cancel each other out, giving:

x * (365/91) = 0.025 * (100,000 - x)

Now, the thing on the right can be changed by multiplying the 0.025 into each of the terms in the brackets:

x*(365/91) = 0.025*100,000 - 0.025*x

x*4.01099 = 2,500 - 0.025*x

Now, you can add something to both sides and it won't change the truth of the equation. So add 0.025*x:

4.01099x + 0.025x = 2,500 - 0.025x + 0.025x

You can see the 0.025x terms on the right hand side will cancel each other out.

4.01099x + 0.025x = 2,500

You should also see that you can add the two x terms on the left hand side together:

4.03599 x = 2500

But you're looking for x rather than 4.03599 x. So divide each side of the equation by 4.03599:

4.03599 x / 4.03599 = 2500 / 4.03599

x = 2500 / 4.03599

x = 619.43

Does that help?

Don't think about "bringing things to the other side" because it reduces it to a meaningless method. Think about adding the same thing to each side, or subtracting the same thing from each side, or multiplying each side by the same thing.

I'm coming after you with my teeth bared...

why do you do this?

You can multiply both sides of an equation by anything and it will still be true. So you can multiply both sides of this by (100,000 - x). YOu'll get:

(x / (100,000 - x)) * (365 / 91) * (100,000 - x) = 0.025 * (100,000 - x)

Sorry for the long delay. That's the trouble with trying to explain something like this, when I'm also busy tidying the kitchen.

You have x / (100000 - x)

That's two different things involving x. So you want to separate them so that you can tackle them independently. You multiply both sides by (100000 - x) so that the (100000 - x) at the bottom of that division sign is eliminated. This introduces a (100000 - x) in other places, but that's OK, because they've been separated from that x at the top of the division sign.

Does that make sense?

aw thanks for coming back so quickly - I was out anyway (we have an annual feast of Goose with some friends)

I'm going to leave it for tonight and come to it fresh tomorrow.
But it does seem to make sense to me.

Any time Sho. What you need is lots of repetition.

There should be a guide entry on simultaneous equations?

If you can handle a single equation you should be able to handle several equations - simultaneously.

The starting point is understanding what is meant by the equality sign - a symbol that tells you the "left hand side" quantity is identical to the "right hand side" quantity. Next you need to learn what is meant by "manipulating the equation" and so forth. There are standard tricks as well as thinking your way through the problem. Anyway gnomon is your man and good luck.

Okay, yes - as gnomon says - it is not a simultaneous equation - just a single equation. So you just need to learn how to manipulate a single equation algebraically.

Isn't it really irritating when everyone gangs up to tell you how simple it is?

I did say I bite...

I know nothing of this subject. All I was going to add was to suggest checking to see if this is covered on the Khan Academy website.

http://www.khanacademy.org/

"Rearranging Equations" e.g.
http://www.youtube.com/watch?v=_WWgc3ABSj4

There are also some examples in the khan website

As gnomon says practice makes perfect.

I have managed to keep myself from butting in for 18 hours now - I think I deserve a badge