Finding the Sum of Two Numbers When Their Product is 1,000

[mustang]

If x and y are whole numbers that don't have10 as a factor, and if xy = 1,000, find x + y.

 

[gnome]

You have 2 integers x and y such that their product xy is a multiple of 10, but neither x nor y is a multiple of 10 (the rightmost digit of the product is 0).

Then the rightmost digit of one of them, let's say y, must be 5, and then x must be an even number. Think about it and you will see that this is the only way to end up with 0 in the 1's column of the product.

So you can express x and y in a different form:
x = 2a
y = 10b + 5
where a is a non-zero integer and b is an integer (maybe 0).

Now, find the product in terms of a and b, set that equal to 1000 & see if that helps you find the answer.

 

[mustang]

The steps.

The answer with the steps to follow.

 

[gnome]

I edited my post. See hints above.