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Assume I have two numbers, say, 23 and 1150. Also assume I have a given percentage, say, 32.6%. What formula would I use to find the number that is 32.6% between 23 and 1150?

CGriffin
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  • You could use a linear interpolation. Let the first number be $a$ and the second be $b$, and let the fraction be $t$ (i.e. you want to find the number that is $t$ of the way from $a$ to $b$). Then, your number is $(1-t)a+tb$. – Michael L. Jun 07 '17 at 15:37
  • 23 + (1150 - 23) x 32.6 / 100 = 435.482, because 23 + (1150 - 23) x 0 / 100 = 23 and 23 + (1150 - 23) x 100 / 100 = 1150. –  Jun 07 '17 at 15:37
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    You've made a calculator error. The answer is $390.402$. – Michael L. Jun 07 '17 at 15:42
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    It is not particularly clear what saying "x % between a and b" is supposed to mean and it isn't a common mathematical expression. As with all math we need to clearify what we mean... and then we do it. If we mean: The difference between a and b is an amount and we want a the number than is x% of that amount above a ... then that is: a + x%of(b-a). – fleablood Jun 07 '17 at 15:47

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The number that is $x\%$ of the way between $a$ and $b$ is given by $$a + (b-a)\cdot \frac x{100}.$$

For example, the number $30\%$ of the way between $10$ and $20$ is $$10 + (20-10) \cdot \frac{30}{100} = 13.$$

Why this formula? The factor $b-a$ gives you the length of the interval. The factor $\dfrac x{100}$ tells you how much of this length you need in order to get $x\%$. Finally, the term $a$ ensures that you start moving "$x\%$ of the way into the interval" from the beginning of the interval.