Neither is more correct than the other. TMTOWTDI, that's all.

I prefer to use the assignment operators because I think they're more intuitive and more idiomatic. And I prefer auto-increment and auto-decrement to the assignment operators. So I'd do this…

    $total_days++;
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…instead of this…

    $total_days += 1;
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…and I'd never do this…

    $total_days = $total_days + 1;
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UPDATE:  I concur with Your Mother's remarks about the concatenation operator. I hardly ever use it. In most cases, there's a better way to accomplish one's string-building tasks using other methods, particularly join().