Find two integers with a sum of 36 and the greatest possible product.

Find the variables

I personally like to use the variable “x”, and since there are two integers that means there are two integers. That means the second variable is (36 – x). For example, if the first variable was 4 and using 36-x, would result in 36 – 4, that means the second variable would be 32.

Variables  

1st x= x

2nd x= 36-x

when it says the greatest possible product, that means that we’re looking for the maximum value.

We put the variables in the factored form.

(x) (36 – x)

1st x = 0

2nd x = 36

Now we need to find the vertex

(1st x) + (2nd x) / 2

0 + 36 /2= 18

(18,_)

Then we input the new “x” value

(x) (36-x)

(18) (36-18)

(18) (18)

=324

So the answer is (18,324).