Kids grow up fast these days. Barely teens and tweens are eager to take part in the activities of their older peers, including romance. Maybe there are kids in your life who are lookin’ for love, and maybe you’re not sure if they’re old enough. I can’t answer that question for you completely, of course, as it depends to some extent on your family’s values. But there is a mathematically provable minimum age for dating, and I am happy to provide the relevant argument as a public service.
We accept as axiomatic the “half plus seven” rule as the lower limit for the acceptable age of a dating partner. Let one partner’s age be [tex]x[/tex] and the other’s be [tex]y[/tex]. Then the rule gives us two inequalities: [tex]y \ge \frac{1}{2}x+7[/tex] and [tex]x \ge \frac{1}{2}y+7[/tex] There are two inequalities because each partner must be of acceptable age for the other. Those two inequalities form a system, which we can solve by graphing them on the same set of axes. The graph of each inequality is a line plus the half-plane on one side of it (indicated by shading). The solution to the system is the intersection of the two graphs. The graph for our system is shown below.
The solution is the purple triangular region, including its boundary lines. The region represents the allowable pairs of ages of the partners in a dating relationship. Note that the point with minimum coordinates in the solution set is [tex](14, 14)[/tex]. Thus, the youngest allowable age for a romantic relationship is 14. If you have a younger child who wants to pursue a crush, simply explain that the immutable laws of mathematics forbid it. I’m sure they’ll understand.
Past 14, though, you’re on your own.
