How would one find the number that is a given percentage between two numbers? 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?

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.
