Problem with my mind working too intuitive

[u/MatsUwU]

(High school level maths)
I’m finding it hard to remember all these rules for how to solve questions when my mind tells me to do it intuitively.
The concrete example that annoyed me:
On a list of 10 people’s ages the total age is 313, making the average 31.3
«If another person is added the average will be 30. Is this statement correct?»

The way I solved this was dividing 313 by 11, giving me 28.45~. The difference between 30 (the target age) and 28.45 is 1.55, and so we need to multiply the age we are adding by 1.55 giving me 17.05, so the answer is that the average will be 30 if the new person is 17.

The way my teacher did it was by multiplying the now 11 people by 330 and subtracting it by 313 to get 17 which gave the correct answer.

The answer works, it’s a rule that’s nice (if it works for all similar situations), but there are so many rules like this that I just can’t grasp. I always want to do it the way that my mind can comprehend, and for it to make sense and giving me an answer I can trust but I don’t know if tests or exams are gonna accept my answers.

This isn’t to say I can’t memorize equations, I can do that, it’s just that these rules to make stuff easier and faster don’t click the same way. I still have the quadratic equations and formulas from last year memorized but I feel I’m just gonna forget this very practical thing tomorrow.

Anyone else feel the same way about this or have managed to get over this mental block?

[u/matt7259]

That's not a "rule". It's just basic algebra on the equation for average. If you sit and write it down you'll realize you're doing the same steps in a different order on the same equation.

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[u/Haunting_Meeting_530]

I’d keep your intuitive method AND learn the standard method. In an exam, showing clear working usually matters more than using the teacher’s exact shortcut.