Question 1168683
<br>
Solve informally and quickly by looking at pairs of positive integers with a product of 204 and finding a pair that satisfies the other condition.<br>
1*204
2*102
3*68
4*51
6*34
12*17<br>
34 is 4 more then 5 times 6....<br>
ANSWER: Kerwin is 6 (his father is 34)<br>
Suppose a formal algebraic solution was required.  Then<br>
x = Kerwin's age
5x+4 = father's age<br>
{{{x(5x+4) = 204}}}
{{{5x^2+4x = 204}}}
{{{5x^2+4x-204 = 0}}}<br>
You could try to factor that; but for most students that would be difficult.<br>
You could of course go straight to the quadratic formula to find the answer.  The use of the formula is straightforward; but in this case the required calculations are not easy.<br>
So at this point, I personally would go to the informal solution shown above to find the answer is x=6, and then I would continue with the formal algebraic solution.<br>
{{{(x-6)(5x+34) = 0}}}
{{{x = 6}}}<br>