Step 1: Remember Addition Rules for Odd/Even Numbers

Firstly, we can look at the odd and even rules involving addition.
Odd Number + Odd Number = Even Number
Even Number + Even Number = Even Number
Odd Number + Even Number = Odd Number

Step 2: Try an Example Problem Or Interpret The Situation
The situation above says we are adding two even numbers to an odd number and then multiplying the result by an odd number. Let’s take this step by step.

Even Integer + Even Integer = Even Integer (New Sum 1)

Since two even integers added together gave us an even integer, we can add this new even integer to the odd number.

Even Integer (New Sum 1) + Odd Integer = Odd Integer (New Sum 2)

Step 3: Multiply the Result from Step 2 by an Odd Number
We can look at the odd and even rules involving multiplication.

Odd Number × Odd Number = Odd Number
Even Number × Even Number = Even Number
Odd Number × Even Number = Even Number

Odd Integer (New Sum 2) × Odd Integer = Odd Integer

We expect the result to be an odd integer

Step 4: Interpret the Information
Since we know that our answer has to be an odd integer, which means a whole number ending in a 1, 3, 5, 7, or 9. Therefore, the correct answer choices that could potentially be the answer to this problem would be 175 and 193.