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# If a changes to b, then doesn't a + d = b? Why a(1 + d) = b? [closed]

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Closed as unclear by Peter Taylor‭ on Mar 23, 2023 at 13:58

This question cannot be answered in its current form, because critical information is missing.

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My 9 year old does not grok DanielWainfleet's answer. How can we intuit why percent change divides the difference by the original number, NOT the new number?

If a changes to b then $\color{red}{a(1+d)=b}$ so $d=(b/a)−1=(b−a)/a$.

Why $\color{red}{a(1+d)=b}$? Why can't this be $\color{limegreen}{a+d=b}$? Isn't it more straightforward to symbolize change as $\color{limegreen}{d}$, rather than $\color{red}{ad}$ ?

If I have 2 apples, and buy 3 more, then my new amount of apples $\color{seagreen}{= 2 + 3 = 5}$. NOT $\color{firebrick}{2(1 + 3) = 10}$.

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