Remembered Test Question?

1. Apr 5, 2006

barcat

I just took a test in Pre-Algerbra. I remember a question that went like this.

"The sum of two numbers is 8"
"The sum of these numbers squared is 40"
"What are the numbers?"

Is the inital equation that I came up with right/wrong?

$$(x^2+y^2)+(x+y)=(40+8)[\tex] Last edited: Apr 5, 2006 2. Apr 5, 2006 barcat OK.........my latex is not working WHY 3. Apr 5, 2006 Hurkyl Staff Emeritus You used the wrong slash. You wanted / And while what you wrote is correct (assuming x and y denote your two numbers), I wonder why you wrote two assertions as one equation. 4. Apr 5, 2006 barcat "The sum of two numbers is 8" "The sum of these numbers squared is 40" "What are the numbers?" Is the inital equation that I came up with right/wrong? [tex](x^2+y^2)+(x+y)=(40+8)$$

OK....I don't know why I did this. I'm afraid I do this too often.

5. Apr 5, 2006

barcat

"I wonder why you wrote two assertions as one equation."

what does this mean?

6. Apr 5, 2006

Hurkyl

Staff Emeritus
In the problem, there were two statements:

"The sum of two numbers is 8"
"The sum of these numbers squared is 40"

So it seems odd that your mathematical model only has one statement:

$$(x^2+y^2)+(x+y)=(40+8)$$

7. Apr 5, 2006

barcat

are you refering to that this can also be written like-

$$(x^2+y^2)+x+y=48$$ ?

8. Apr 5, 2006

d_leet

No he means that there are two seperate statements and you have no reason to combine them, so why are you?

9. Apr 5, 2006

barcat

Ok...........like most of the other students in my class............I have know idea of what you are talking about. Are you saying to write it like this-

$$(x+y)^2+x+y=48$$

my major problem in understanding this is understanding the terminology.

10. Apr 5, 2006

barcat

"No he means that there are two seperate statements and you have no reason to combine them, so why are you?"

If they have the same variables...........how can you not?

11. Apr 5, 2006

barcat

Are you saying-

$$(x+y)^2+x+y=48 ?$$

Last edited: Apr 5, 2006
12. Apr 5, 2006

barcat

Is there a differnce if I write it like-

$$(x^2+y^2)+x+y=48$$

13. Apr 5, 2006

barcat

did I say something wrong?

14. Apr 5, 2006

Hurkyl

Staff Emeritus
Very easily: by not doing it.

x² + y² is certainly different than (x + y)². (But that has nothing to do with what we're saying)

15. Apr 5, 2006

barcat

Too many ridles...............I have been at this for 4 days.
Are you saying that there are 4 different variables?

16. Apr 5, 2006

Hurkyl

Staff Emeritus
I think you have the variables right: one variable for each of the numbers you're looking for.

But the problem made two statements about them. So, you should have two equations!

17. Apr 5, 2006

barcat

OH...........X is the answer to the first statment, and Y is the answer to the second?

18. Apr 5, 2006

Hurkyl

Staff Emeritus
The first step is not to answer the question. The first step is to translate the question into a mathematical problem.

19. Apr 5, 2006

barcat

$$x+x=8$$
and
$$y^2+y^2=40$$

20. Apr 5, 2006

barcat

$$x+y=8$$
$$x^2+y^2=40$$