if we know someone lost $2 and that loss was a 2.4% loss from the starting investment to the exit, can we figure out the starting and ending money involved?
Thanks for providing this description which makes things more clear. When writing this you (probably) used the correct phrasing without realizing it, "percentage loss from starting investment to exit". In this circumstance the percentage will be relative to the original investment.
BUT to add to the confusion you seem to have swapped the numbers around. I'll assume that you meant to say, "if we know someone lost
$2.4 and that loss was a
2% loss from the starting investment to the exit"
Now we can calculate the amounts with some extra certainty...
X=Amount originally invested
Y=Returned amount at exit
[math]X-Y=2.4 \,[/math] (amount lost)
[math]\dfrac{100(X-Y)}{X}=2 \,[/math] (percentage loss from starting investment to exit)
Reading between the lines it seems that you're not a math student, so I'll work it out for you. Substitute Y=X-2.4 into the second equation to obtain...
[math] \dfrac{100(X-(X-2.4))}{X}=2 [/math]
[math] \dfrac{100(2.4)}{X}=2[/math]
[math]100\times2.4=2X[/math]
[math]240=2X[/math]
[math]X=120[/math]
Putting X value back into the first equation gives...
[math]120-Y=2.4[/math]
[math]Y=120-2.4[/math]
[math]Y=117.6[/math]
NOTE: percentage calculations depend on the wording and context to avoid ambiguity
NOTE2: If the numbers are actually the other way around, then hopefully you can now repeat the procedure above yourself using the different numbers.