# The 'Dating Rule'

*Two things: the somewhat random-looking picture above is from The Moon Is Blue, a 1953 film that’s the first known reference to the ‘dating rule’ discussed here. Secondly, I don’t make any judgement about the validity of the ‘dating rule’ - you might find it a useful rule of thumb or a ludicrous restriction; I find it a nice thing to do some algebra on.*

There is a so-called rule about dating: the youngest age you are supposed to date is half your age plus seven. So, if you’re 16, the youngest age you should consider is 15 – because 16 divided by two is eight and 8+7 equals 15.

We can write the dating rule as an equation: $y=x \div 2 +7$. In this equation, $x$ is your age and $y$ is the minimum age you are supposed to date. Why would we want to do this? Well, it means we can work out some other implications of the rule.

For instance, you might want to know what the oldest age you could reasonably date would be. The rule doesn’t say anything about that, but it does also apply to the other person. So if you’re 13, you can date anyone over $13 \frac{1}{2}$. But the $13 \frac{1}{2}$ year old can only date people who are at least $13 \frac{3}{4}$ – so you can date them, but they can’t date you.

How do we work that out? Well, we need to rearrange the equation. In this case, we want to solve for $x$. We take away seven from each side to get $y-7=x \div 2$, and then double both sides to get $2y-14=x$. That means, to find the oldest age you can date, you have to double your age and take away 14.

So, if you’re 16, the minimum age you’re supposed to date is 15; the oldest is 18.

If you’re 13, you’re out of luck. The youngest you can date is 13 1/2, but the oldest is 12. So even somebody your own age is simultaneously too old and too young for you. Nightmare!

It turns out that the minimum age this rule allows dating is 14 – for extra credit, can you explain why?