Basic Algebra Word Problems 1

>> I'm going to go over some basic word problems,
which it's even better to think of these as puzzles or riddles,
so these will be algebra problems with one variable.
And we'll be talking about how to set up the problem
and then solve and check it.
So here's one.
If I add 20 to John's age, I get 32.
How old is John?
All right.
The key is to read the problem,
and then see what you're looking for.
How old is John?
So we're looking for John's age.
So let's set up a variable.
Let's call it J, that will be John's age.
And now you could use X if you want.
Now it says, if I add 20 to John's age, I get 32.
So if I add 20 to John's age --
so I have to start out with John's age
and I have to add 20 to it.
All right.
Which means, plus 20, it says, I get 32.
What does that mean, I get?
It means, its equal.
So that word, get, in this case, really means, equal 32.
So there's the equation.
Now we could solve this pretty easily by just subtracting 20
from both sides, and we get J equals 12.
So it looks like John is 12.
All right.
Now this is a word problem so you have
to answer your problem in words.
John's age is 12 or you could say, John is 12 years old.
Now we can check it, which is a good idea.
This one's pretty simple to check.
It says, if I add 20 to John's age.
All right.
So we're going to start with john's age,
which we think is 12, and we're going to add 20, and we get 32.
And it says that, when I add 20, I should get 32.
So that's how you check it.
You don't go back to the equation
because maybe you wrote the wrong equation.
You go back up to the words of the problem and do some sort
of check to make sure it all makes sense.
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Here's another word problem.
10 less than a number is 18.
What is the number?
Again, you read the problem through, and what is it
that you're looking for?
You're looking for a number.
So how about we define --
this is called defining your variables.
It means you have to let some variable represent what you're
looking for.
Let's call the number, N. N for number.
Okay. Now this is a little bit tricky.
10 less than a number, that means the number's bigger,
right, than 18 because I'm going to subtract to get 18.
All right.
So 10 less -- most people do this incorrectly
and write 10 minus N. That's wrong.
Okay. What it's saying is 10 less than something.
It means that I've got to have something and then take away 10.
It's really tricky.
So when you see 10 less than a number, it means you're going
to take 10 away from something.
Okay. Tricky problem.
So we're going to take 10 away from a number, right,
and we call the number, N. Okay.
So there we are.
So N minus 10.
So we've got 10 less than a number is --
the word, is, in this case, just means equals 18.
So what happens is we're breaking
up this problem into two parts.
The part before the word, is, is what will go
on the left side of the equal sign.
And the part after the word, is, will go after.
All right.
So now we need to solve the problem.
Let's add 10 to both sides to solve for N.
So we get N equals 28 and, remember,
this is a word problem.
We don't write N equals 28.
Look at the word problem.
It does not say find N. It says, what is the number?
So let's write that down.
The number is 28.
Now I know I haven't checked it
yet so this might not be correct,
but I'm hoping it's correct.
So let's do a little check.
All right.
It says, 10 less than a number is 18.
Well, if the number is 28, 10 less than that means I'm going
to subtract 10 from it, right, and I get 18.
So there you go.
Now both of these problems you probably could have done
in your head, but what we're doing is practicing doing easy
problems so when it gets to something that we can't do
in our head, we could use the same technique.
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Next problem.
Mary's weight decreased by 14 pounds is 109.
How much does Mary weigh?
Again, read through the problem and look
to see what you're looking for.
You're looking for Mary's weight, right, because it says,
how much does she weigh?
So how about we say Mary's weight is -- how about W?
Remember, it's up to you what variable you want to use.
Now this is a little bit tricky.
It says, Mary's weight decreased by 14.
So that means we're going to start off with her weight
and then take away 14.
It's being decreased.
Decreased by, means subtract that number,
14, from Mary's weight.
So we're going to say -- and also keep in mind the, is,
right here, is the equal sign, right,
that's going to be our equal sign.
So we've got the part before the equal sign, which is going
to be Mary's weight decreased by 14 pounds.
So what would that look like?
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Mary's weight decreased by --
take away 14, and then we've got the equal sign,
right, for the is.
And on the other side, it's just 109.
So there's our equation.
All right.
Pretty easy to solve.
We're just going to add 14 to both sides and we solve
for W. Now, remember, the answer is not W equals 123.
The question is: How much does Mary weigh?
So we say, Mary weighs 123 pounds.
We're talking about weight and we're talking about pounds;
so you want to complete the problem.
You might not have to put an entire sentence but you should,
at least, write the 123 pounds.
Don't leave it as some variable equals a number.
Now let's check it over here.
It says, if we take Mary's weight,
which we decided was 123, and we decrease it
by 14, well, what do we get?
You get 109, and it says that's what we should get.
We should have gotten 109, right, so it does check
and that's our answer.
All right.
Next one. If I divide Tom's age by 7, I get eleven.
How old is Tom?
All right.
So we read through it.
What are we looking for?
We're looking at how old Tom is.
Well, that will be Tom's age, right,
so we have to define Tom's age by something.
How about T, for Tom's age?
All right.
Now this is a little bit tricky.
It says, if I divide Tom's age by 7, I get 11.
So we want to start off with Tom's age and divide by 7.
So we're going to take T, divide it by 7 and it says, I get 11.
I get, means, equals 11.
Now there are a couple of ways to solve this problem.
One is to multiply both sides by 11.
I'm sorry.
To multiply both by 7 so that the 7 and then this T cancels.
So let's do it that way.
Let's multiply both sides by 7 so that those cancel,
and I'll solve for T. So I have T equals 77.
So that's what we're looking for.
We are looking for T, Tom's age.
So we would say, Tom is 77 years old.
And, of course, we want to check it.
All right.
So if I take Tom's age, which is 77,
and if I divide by 11, what do I get?
What's 77 divided by --
I'm sorry, by 7, that's what it said.
So you have to read the problem carefully.
By divided by 7 -- so what's 77 divided by 11?
I'm sorry.
Divided by 7, it's 11.
So, yes, it does check out when I divide it by 7, I get 11.
I think that was tricky doing a problem with 7 and 11's in it.
Let's do one more.
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Here it is.
If I multiply a number by negative 5, I get 35.
What is the number?
All right.
We're looking for a number again.
So let's define the number -- let's use N for the number.
All right.
It says, if I multiply a number by negative 5, so that means
that I have to multiply N times negative 5,
which we usually write
as negative 5 times N. Negative 5N means negative 5 times N. It
would look funny if you wrote N with a minus 5 next to it,
it might look like N minus 5, which is, well, it's the same
as multiplying those two together.
So negative 5N -- and what do you get?
You get 35.
All right.
So how do we solve that?
Divide by negative 5.
So N is negative 7, so then the number is negative 7.
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So we could check that.
It says, if I multiply the number by negative 5, well,
the number negative 7 times negative 5 does give you
positive 35.
And there you go.
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