SOLUTION: the sum of two numbers is 12. their product is 32. find the numbers. not good at word problem so i am have trouble setting it up. once i get it set up i can work its just braking

Algebra ->  Pythagorean-theorem -> SOLUTION: the sum of two numbers is 12. their product is 32. find the numbers. not good at word problem so i am have trouble setting it up. once i get it set up i can work its just braking       Log On


   

Question 203082: the sum of two numbers is 12. their product is 32. find the numbers.
not good at word problem so i am have trouble setting it up. once i get it set up i can work its just braking it down to set it up. please help.
Found 2 solutions by jim_thompson5910, PRMath:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let

x = first number
y = second number


"the sum of two numbers is 12" translates to x%2By=12

and "their product is 32" means that xy=32


So you basically have the system


system%28x%2By=12%2Cxy=32%29


I'll let you take it from there. Let me know if you need more help.

Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
There are probably lots of ways to do this but I solved this as a system.........

For example, I broke down the phrases like this:

The sum the sum of two numbers is 12: X+%2B+Y+=+12
their product is 32: %28X%29%28Y%29+=+32+


Then I took the first equation:
X + Y = 12 and solved for X ===> X = 12 - Y

THEN I substituted that info into the 2nd equation:

%28X%29%28Y%29+=+32
%2812-y%29y+=+32 (see where the (12 - Y) was substituted in for "X"?)
12y+-+y%5E2+=+32 (distribute the "Y" to 12 and -y)

Now it gets tricky.... I see I have -y%5E2 and I don't want that, so I am going to move it to the other side of the equation so that I can work with a POSITIVE y%5E2. I'm also going to move the %2B12Y by subtracting it from both sides.
0+=+y%5E2+-+12Y+%2B+32 (I subtracted 12Y and added y%5E2 to both sides)
0+=+%28Y+-+4%29%28Y+-+8%29 (Factored the answer)
Y = 4 Y = 8
Does this check? 4 + 8 = 12 AND 4 times 8 = 32.
So yes, this does check.

Now I have left out some explanations, because you said you needed help setting it up and not so much help working the problem. I hope this is enough of an explanation.

Good luck and I hope this helps....