# Thread: Find the Larger Integer

1. ## Find the Larger Integer

The product of two integers is -40. If the same two integers are added, their sum is -3. Find the larger of the integers.

I did this:

x*y = -40...Equation A
x + y = -3..Equation B

I solved Equation B for y and got y = -x - 3.

I plugged the value for y into Equation A and solved for x.

x(-x - 3) = -3

-x^2 - 3x = -3

I moved everything to the right side.

0 = x^2 + 3x - 40

My final answer is 5 but the math book tells me that the correct answer is -8. Can you explain who is right and why?

2. Depends on whether they mean "largest" in the sense of "absolute value" (in which case it's -8) or "largest" in the sense of "most positive". Go back thru the book and see how they define "largest".

3. Originally Posted by sharkman
The product of two integers is -40. If the same two integers are added, their sum is -3. Find the larger of the integers.

I did this:

x*y = -40...Equation A
x + y = -3..Equation B

I solved Equation B for y and got y = -x - 3.

I plugged the value for y into Equation A and solved for x.

x(-x - 3) = -40

-x^2 - 3x = -3

I moved everything to the right side.

0 = x^2 + 3x - 40

My final answer is 5 but the math book tells me that the correct answer is -8. Can you explain who is right and why?
Note the minor correction above.
But, yes you are correct.

EDIT: I think that "largest" means largest.

4. ## ok but...

Originally Posted by Plato
Note the minor correction above.
But, yes you are correct.

EDIT: I think that "largest" means largest.
Are you saying that the equation x(-x - 3) = -40should not be equated to -40? But the question stated that the product of two integers is -40. I moved everything to the right side and so -40 remains -40, right? Please, explain what you meant by "minor correction" in your reply. Thank you.

5. Originally Posted by sharkman
Are you saying that the equation x(-x - 3) = -40should not be equated to -40? But the question stated that the product of two integers is -40. I moved everything to the right side and so -40 remains -40, right? Please, explain what you meant by "minor correction" in your reply. Thank you.
You had $\color{red}x(-x-3)=-3$.
You had $\color{red}x(-x-3)=-3$.