What is this called? (Equations involving percentages)

Question

I am trying to describe our formulas to our users, and have forgotten the basic math term for these 2 types.

First one is: $$y=x+10\% $$ $$z=y+10\%$$ if $x$ was $10$, then $z$ would be $12.1$.

Other is: $$p=10\%+10\%+10\%\;\;\;\; (30\%)$$ $$z=x+p$$ if $x$ was $10$, then $z$ would be $13$.

I'm drawing a complete blank, and appreciate any help in wording this and giving a 'proper' example to my users.

Thank you Stack community in advance,

Answer 1

It looks like you're describing increasing a number by a percentage. Mathematically the first would be written y = 1.1x, z = 1.1y (which gives z = 1.21x, so your example with x = 10 and z = 12.1 is correct). The second would be written $z=x\times(1+0.1+0.1+0.1)=1.3x.$

Answer 2

I would call the first "basic calculator notation". Open Windows calc.exe in "standard" rather than "scientific" mode and type 1 0 + 1 0 % + 1 0 % = and you will get 12.1, though note that if you were to type 1 + 2 * 3 = you would get 9, which is not encouraging.

The second is a mixture of what I would call "mathematical notation" and of the first form. I would say $10\% +10\% +10\%=30\% = 0.3\,$ (though it would not if you tried it in calc.exe, which instead gives 0).

Another way of looking at this is that the first form calculates compound percentage increases while the second does simple percentage increases. But I suspect that trying to learn the difference is more likely to lead to confusion than shortcuts.

Better to avoid using percentages like this and instead turn to decimal, so the first becomes $10 \times 1.1 \times 1.1 = 12.1$ while the second becomes $1 0 \times ( 1 + 0 . 1 + 0 . 1 + 0 . 1 ) = 13$.