struggling with simultaneous equations?

Are any of you struggling with the simultaneous equation question in your first 109 Quantitative Skills workshop?

A big challenge for you guys is translating a biology scenario into a mathematical form that can then be solved... Here is a really simple example:

Question: A man owns 18 pets. These pets are cats and birds. If the pets have a total of 56 legs (assuming non of the birds legs are sticking out of the cat's mouths!), how many cats and how many birds does the man own?

Ok, so we want to find out how many birds and how many cats this man owns.

First of all you have to try to express this information using a couple of equations:

Lets use the letter x to represent how many cats the man owns
and lets use the letter y to represent how many birds the man owns.

So, from the information we know that since the man has a total of 18 pets, our first equation can be:

x + y = 18

And we also know that in total all the pets have 56 legs combined, and we know that cats generally have four legs and birds have two. So our second equation can be:

4x + 2y = 56

Excellent, now we have two equations and each equation has two unknown variables for us to find.... this is how I would solve them:

x + y = 18 - equation 1

4x + 2y = 56 - equation 2

I would rearrange equation 1 to:

x = 18 - y 

Then I would substitute the 18 - y into the second equation:

4 x (18 - y)  + 2y = 56

And then I'd solve this new equation to find y:

4 x (18 - y)  + 2y = 56

72 - 4y + 2y = 56

 - 4y + 2y = 56 - 72

- 2y = - 16

y = - 16 / - 2

y = 8

So we now know that the man has 8 birds.

Now we need to find out how many cats the man has, we can figure this out using equation 1:

x + y = 18

x + 8 = 18

x  = 18 - 8

x  = 10

Now we also know that the man has 10 cats.

It is always a good idea when you do a question like this to check your answer. You can do this by putting the values you found back into one of your original equations:

4x + 2y = 56

4 x 10 + 2 x 8 = 56

40 + 16 = 56

I hope that helps