[Math] Adding up numbers * weights to get a result (not weighted average), does it have a meaning

Question

I have been comparing two solutions and used weights for individual areas based on their importance. I was interested which solution is better, i.e. which one has the higher score.

The thing is I simply multiplied each score with individual weight (Security with 0,8, UI with 0,2 etc) and then summed them all up and compared. Does it make sense or I need to use weighted average?

In the following example, why the authors used weighted average and not simply multiplied and sum up results using 0.5 etc instead of 5?

E.g.:

Answer 1

If the sum of the weights is in both cases the same (e.g. 1), you can do it like you did, otherwise you should use the weighted average.