Word problems and Linear systems.

[Ryan C]

Hi, I'm looking to receive a little help with this area of math. (My math skills are very poor, (currently repeating 10th grade math ))

To avoid 'cheating' on my math homework, I'll change a few variables etc, to make the problem acceptable:

"A waitress earned $55 in loonies and toonies. There are a total of 38 coins, how many of each did she have?"

I honestly don't know where to start; my guess is:

Let 'x' represent the loonies.
Let 'y' represent the toonies.

x + y = 38

From this point on, I am stuck.

Any help would be great, thanks.

~ Ryan

 

[arildno]

Well, how many dollars does a single "loonie" and "toonie" represent?
I'm not an American..

 

[SnipedYou]

Does the problem also give you the value of the coins?

Here let me give you a sample problem here: Let's say I have a total of 1 dollar. Let's say I have a total of 15 coins in both nickel and dimes. Well I'll let my nickels be my x's and my dimes be my y's. Now we get the equations:

$$x + y = 15$$ and
$$5x + 10y = 100$$

With some subtraction we can get $$y = 15 - x$$
Now we can substitute $$5x + 10(15 - x) = 100$$
$$5x + 150 - 10x = 100$$
$$-5x = -50$$
$$x = 10$$
Now I'll substitute this into the original equation:
$$10 + y = 15$$
$$y = 5$$
We find that we have 10 nickels and 5 dimes (hope this helped)

 

[Ryan C]

Loonies are $1 each, toonies are $2.


@SnipedYou: I don't see where the '100' came from in your bottom equation. Unless it means 100 cents.

 

[SnipedYou]

Ok so now we will have

x = loonies
y = toonies
$$x + y=38$$ and
$$x + 2y = 55$$

Then let's solve for either x or y (I'll do it for x)
$$x = 38 - y$$ Then we'll substitute:
$$38 - y + 2y = 55$$
Simplify: $$y=17$$
Now substitute into the our equation: $$x + 17 = 38$$

and we find that $$x = 21$$

 

[Ryan C]

Thanks that really helped. It's the setting up of the equation that gets me everytime.

 

[HallsofIvy]

Well, how many dollars does a single "loonie" and "toonie" represent?
I'm not an American..

It's not a matter of American! Loonies, at least, are Canadian- their "dollar" has a picture of a Loon (that's a bird) on it.

 

[arildno]

It's not a matter of American! Loonies, at least, are Canadian- their "dollar" has a picture of a Loon (that's a bird) on it.

Well, I'm not Canadian, either.
However I must protest; the loon is not a loony, it is a very level-headed bird.
In Norwegian, it is called a "lom".

 

[Diffy]

Let 'x' represent the loonies.
Let 'y' represent the toonies.

x + y = 38

One thing that helps me... You need to be VERY clear when you define what your variables are.

You want 'x' to represent the number of loonies.

Let 'x' represent the loonies. This could mean anything, such as the number of, the value of, the color of, etc. If you are clear in defining your variables you can work out sentences that will help you solve them.

For Example:
"I know that the number of loonies I have plus the number of toonies I have equals thirty 38."

Now that you have loonies and toonies clearly defined this sentence can be converted to an equation MUCH easier.

x = the number of loonies.
y = the number of toonies
equals = '='
plus = '+'

x + y = 38

If you have CLEAR definitions, you can literaly talk out the problem, to form your equations that need to be solved.

 

[arildno]

A very relevant and important post, Diffy!
To develop the mental discipline required to formulate precisely what you mean is actually THE biggest challenge for most people to master maths, in my opinion.