3. The difference between two positive integers is 7 and their product is 198 Use algebra to work out each integer.

<p> <br />Given two positive integers, let's assume X and Y. The problem states that their difference (X-Y) is 7 and their product (X*Y) is 198.<br /><br />We need a systematic approach using algebra to work out these integers:<br /><br />1. Start to solve for either of the variables X or Y from the first equation (X-Y=7), assume we're solving for Y. We can rewrite the equation like Y = X - 7.<br /><br />2. Use Substitution method. Substitute Y in the second equation (X*Y=198) with the assumed expression of Y (which was derived from X-Y=7), the resulted equation: X*(X-7)=198. Now we got a quadratic equation that can be solved for X.<br /><br />3. Simplify the quadratic equation and reorganize it to get X^2 - 7X - 198 = 0.<br /><br />4. Factor the equation, from factoring the equation we are able to have the solutions. But upon getting the solutions you remember it is stated “positive integers” hence look for the X that yields positive for both Y & X. <br /><br />Thereby obtaining the two integers values of X and Y that harmonize the initial problem conditions (X-Y=7 and X*Y=198).<br /><br />This is how we use algebra to work out each integers. Basically, algebra is like a puzzle, where you replace your unknown with your known.</p>