If two integers add up to 35 and their product is 304. What are the numbers?

The two numbers have a sum of 35. Let one of the numbers
be x.

Therefore the other number is 35-
x

Now we know that the product of the numbers is 304.
Therefore (35-x)*x = 304

=> 35x – x^2 =
304

=> x^2  - 35x + 304
=0

=> x^2 – 16x – 19x +304 =
0

=> x(x-16) -19(x -16) +304
=0

=> (x-16)(x-19) =
0

Therefore x can be 16 or
19.

So the required numbers are 16 and
19.