# Thread: Find the Smallest Integer

1. ## Find the Smallest Integer

The product of two integers is -24. If the same two integers are added, the sum is -23. Find the smallest of the two integers.

This is what I did:

x*y = -24......Equation A
x + y = -23...Equation B

I solved Equation B for y and got y = -x - 23.

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

x(-x - 23) = -24

-x^2 - 23x = -24

I moved everything to the right side.

0 = x^2 + 23x - 24

My final answer is -24 but the math book tells me that the answer is -23. Can you please explain who is right and why?

2. Originally Posted by sharkman
The product of two integers is -24. If the same two integers are added, the sum is -23. Find the smallest of the two integers.

This is what I did:

x*y = -24......Equation A
x + y = -23...Equation B

I solved Equation B for y and got y = -x - 23.

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

x(-x - 23) = -24

-x^2 - 23x = -24

I moved everything to the right side.

0 = x^2 + 23x - 24

My final answer is -24 but the math book tells me that the answer is -23. Can you please explain who is right and why?
You are right, because (-24)*(1) = -24 and (-24) + 1 = -23... just like the statement of the problem demands.
-23 does not satisfy given conditions.

3. ## I knew it!

Originally Posted by Isomorphism
You are right, because (-24)*(1) = -24 and (-24) + 1 = -23... just like the statement of the problem demands.
-23 does not satisfy given conditions.
I better get a new math book. Why do so many books have errors in the answer section?