Printable View
Okay...I hope I'm putting this topic at the right spot. *stares* Hmm...Oh well, Anyhow, I was wondering if anyone in here is great at math. Like are ya confindent w/ your math skills.
http://i3.photobucket.com/albums/y63/SasukeLUV/math.jpg <--Something like this?
My algebra teacher was fond of saying "The problem with word problems is, there's too many words". I'm not sure how this piece of advice is applicable to the situation at hand, but the man was brilliant, and his genius deserves to be exposed to the world.
Alebgra needs to be picked apart and completed methodically to find the logic behind some of the problems. Figuring out what they're asking for is the biggest part of the problem, I think. For example, problem 2-2 reads (and I'm going to try to be is descriptive as possible):
What is the only pair of integers (x,y) for which twice the square of the first equals three times the square of the second
Picking it apart will tell you that you're trying to find the value of two variables. In addition, the sentence more or less gives you the structure of the equation.
What is the only pair of integers...
You have two variables (pair)
...for which twice the square of the first[variable] ...
2x2
...equals...
This literally translates into an equal sign (=)
...three times the square of the second [variable] ...
3y2
You'll end up with the following equation:
2x2 = 3y2
And you can solve from there.
In problem 2-4, the wording can be tricky if you haven't seen it before.
The squares of two consecutive positive integers.
When you're dealing with a problem where it asks for consecutive integers, (i.e. 1 and 2, or 778 and 779, for example), these are represented in the equation by x and x+1 (do you see the logic behind this?). If the problem specifies consecutive odd or even integers (i.e. 2 and 4, or 17 and 19, for example), these are representated in the equation by x and x+2. Got it?
The problem reads:
The square of two consecutive positive integers differ by 1987. What is the sum of these two integers?
You know you have two "variables" (okay, so it's one variable, but that's not important) in the equation, (x, x+1), because of the two consecutive positive integers part. Keep in mind, though, that the problem asks for the squares of these variables. Thus, you'll be working with x2 and (x+1)2 which FOILs (do you know how to FOIL?) out to x2 + 2x + 1.
Now, let's look at another part of the problem:
...differ by 1987...
The "differ" part implies that there's a difference between the two values, and that difference is 1987. Because of that, it's logical to think that if you subtract one value (the lesser value) from the other (the greater value), you'll get 1987 as an answer. Since x+12 is no doubt the greater value, we'll subtract x2 from it. Let's set it up:
(x+1)2 - x2 = 1987
From there, we can FOIL (like I showed you above), and we get:
(x2 + 2x + 1) - x2 = 1987
*Note that x2 + 2x + 1 is just the FOILed version of (x+1)2. They're completely equal in value.
From there, we'll just simplify. The positive and negative x2's cancel out, and you'll get:
2x + 1 = 1987
Then you just subtract 1 from each side, to leave 2x by itself on the left side of the equal side. You'll get:
2x = 1986
After that, all you have to do is divide everything by two to get x by itself. So, the value of x is...
x = 993
And x+1 is 994, so your two consecutive integers are 993 and 994. Let's go back and check to make sure.
9932 = 986,049
9942 = 988,036
988,036 - 986,049 = 1987
It all checks out.
I'mma stop there for now and wait for a reply.
Brilliant work Sepho. Excellent! :D
I'm going to try and figure out 2-5, 'cause I know it's got something to do with intergration...
Thank you :)
Try 2-4 while you're at it. I ran out of time earlier, but I'm going back to 2-4 right now and I can't solve it.
I end up with:
EDIT: Now that that issue is taken care of, I'll post how to setup the problem back in the first post.
Sepho, I think you got caught by your own explanation - it asks for two consecutive positive integers, so it would be x, x+1 rather than x, x+2, which works out to a whole number.
But, but, but...
If the integers are both positive (or odd), they would have to increment by 2 (x, and x+2). If they incremented by 1, then one integer would be odd, and the other would be even.
But, it only requires that they be positive (i.e. x > 0), not that they both be even or odd. It specifies that they be consectutive, so they would only be one whole number apart.
Okay, okay, okay.
I for some reason keyed in on the positive part and my mind started to play tricks on me. Okay then. The problem is easy enough once that's out of the way.
I thought I was going insane. G'job.
O_O *in shock & already insane* What?!! Oh,......I got it. >.> I think. Yea....Anyhow, thanks a lot you two. >( =o])
++ EDIT: Haha. I found all the answers to the problems. And it's 100% I did a research online and found it..
http://www.mathleague.com/hstest/87-...-solutions.htm
So proud of myself. :love: