A Math Problem

[1241Penguin]

Hello GTPlanet!

After writing a relatively easy math test (or so it seems), many of us (my classmates and I) were surprised to find that our answers for a question was deemed incorrect by the teacher. Here is the original question, as it's written on the test paper:

The sum of the squares of two numbers is 74 and the difference of their squares is 24.

a) What systems of equations models this situation?
b) What are the two numbers?​

This question is not difficult. In fact, I'd say it's quite easy. However, there is still some argument on what the proper response should be.

Pay attention to b), as this is where all the disputes began. Also pay attention to the way you present your answer.

After some time, I'll post the answer the teacher wants it, and the answer we put down, and we can debate who's right, because quite a number of us think that the question could have been worded much better.

 

[Dalamar]

5 and 7?

Edit: Does she want the numbers in order? Hence 7 and 5?

 

[Daniel]

It's a trick question - the answers are 74 and 24

 

[niky]

x2+y2=74, x2-y2=24, thus 2x2=49, thus x=7, y=5

Didn't even have write it down.

BUT:

The answer to b.) is primes.

That's right, right?

 

[Solo]

Odd numbers? Single digit? Finite?

 

[Dalamar]

Oh actually the two numbers could be either x = 7 or x = -7 and y = 5 or y = -5.

Absolute values being 7 and 5.

 

[1241Penguin]

So far, none of you have what my teacher wants (it's a he by the way). But do try again.

I'll reveal the "right" answer after about 5 more responses.

 

[niky]

Primes or odd are both correct.

 

[Dalamar]

Unknowns?

 

[1241Penguin]

The answer involves numbers only (for lack of a better term), no words.

 

[Swara]

Hmm... I'll try to solve this tomorrow

 

[Lucas]

Oh actually the two numbers could be either x = 7 or x = -7 and y = 5 or y = -5.

Absolute values being 7 and 5.

This is what I got right now.




I'm intrigued by the fact you talked about the wording of the problem. I'm quite eager to see what your teacher actually asked for. Maybe Famine could put some light on the issue? 💡




EDIT:

 

[KAWIGREEN23]

X = {-7,7} and Y = {-5,5}

 

[1241Penguin]

Most of you actually got the correct values: +/- 7 and +/- 5. In fact, that is exactly what I wrote on the test. However what the teacher wants is this:

7 and 5
7 and -5
-7 and 5
-7 and -5

We had to write exactly that. And that is where the disagreements begin: is that really what the question asked? We argued that the question was poorly worded to being with. We also argued that the answer had more than "two numbers".

As I was solving this problem, I came up with +/- 7. I knew that the "two" numbers couldn't both be +/- 7, so I was already confused by that; I knew there had to be at least "two numbers" to the solution.

Discuss.

 

[niky]

It was poorly worded. The correct question would be: Solve for all possible values of the two unknown numbers.

As for the answer format, the four phrase answer is the more exact way to say it, but I find yours acceptable.

 

[Dalamar]

7 and 5
7 and -5
-7 and 5
-7 and -5

Maybe you should teach your teacher some Boolean algebra

(7 and 5) or (7 and -5) or (-7 and 5) or (-7 and -5) = (7 or -7) and (5 or -5)

 

[1241Penguin]

His argument against what I said about how there are more than two numbers to the answer is that each pair (i.e. 7 and 5) are "two numbers". Confusing, eh?

 

[Dalamar]

You won't win this argument with the teacher. Maybe it is the way the answer is written in the text book he copied the question from.

 

[Omnis]

Most of you actually got the correct values: +/- 7 and +/- 5. In fact, that is exactly what I wrote on the test. However what the teacher wants is this:


We had to write exactly that. And that is where the disagreements begin: is that really what the question asked? We argued that the question was poorly worded to being with. We also argued that the answer had more than "two numbers".

As I was solving this problem, I came up with +/- 7. I knew that the "two" numbers couldn't both be +/- 7, so I was already confused by that; I knew there had to be at least "two numbers" to the solution.

Discuss.

But you wrote what the teacher wanted. See below.

Maybe you should teach your teacher some Boolean algebra

(7 and 5) or (7 and -5) or (-7 and 5) or (-7 and -5) = (7 or -7) and (5 or -5)

+rep

Bring it to the dean or a (the) principal if you have a problem. Don't chicken out. Any reasonable person would not mark your answer wrong if you put ±5 and ±7. My friend is a doctor of mathematics so he is your friend by proxy, meaning you have more street cred than your teacher.

 

[1241Penguin]

To be honest, it's very unlikely that I will talk to the principal about this since one, it doesn't really affect my overall grade, and two, principals tend to side with the teachers. Trust me, I've seen it happen even in the most ridiculous of situations. And also because he's pretty stuck-up.

I mostly made this thread to see who's right and who's wrong.

@Dalamar: It did indeed come from the textbook. But textbooks can be wrong too, right?

 

[niky]

We had a teacher who marked on guy wrong on the finals on one question. His answer was right, but it wasn't the one she wanted. He failed the entire course by exactly that margin. One point on the finals.

The funny thing is, his answer was right according to THE textbook, but not according to her alternate textbook. Yes, she was an absolute 🤬

And the inspiration for the thread "The _____ of _____ is characterized by _____, _____ and _____."

 

[1241Penguin]

How 🤬 was he when he found out?

 

[niky]

He was pretty demolished. I was standing beside him when he was arguing his case.