I do not arrive has to know how to obtain the rule of three (or of four??) who would allow me to resolve this problem:

I wish to give a 50 % discount has to exploit on a service (no matter its price) which will be executed in 90 days. However I agree to grant this discount only if we make me pre-orders which will be taken into account at the latest until the 80th day. From the 81th day it is not possible any more to make of pre-order) and the customer will pay his service to the normal price.

In summary if we pre-order me the service from the 1st day the customer obtains 50 % of discounts and if we order it to me last days (thus the 80th) he receives all the same 10 % of discounts.

From then on the maximal discount which I grants is 50 % and the minimal of 10 % thus how to apply the rule of three to know the discount has to grant to one the other period? For example what will be the discount which I should grant after 67 days??

If am not wrong the values have to take into account here are:

Maximal discount
Minimal discount
The day of the end of pre-order
The day of the execution of the service

I am suck in math and there it is an immense puzzle...

All values of discounts and deadlines which I indicated are called changed according to the services has to executer, that is why I would like to know the math method for obtain a result with different discounts and deadlines and not only the result for 67 days.

Anybody would have you he an idea for this thorny problem?? My brain is in fusion having to try vainly to look during almost 1 hours..

Thank you in advance for your help