How to calculate the differential payment for a service by several consumers?

Question

Mathematics

There are Q consumers of the service. Consumers are divided into three categories. Each category has its own fee for the service.

Q = Q1 + Q2 + Q3 (in three categories)

Total cost of the service:
X = P1 * Q1 + P2 * Q2 + P2 * Q2
where X is the cost of the service,
P1 is the payment of one service consumer from category 1,
Q1 is the number of consumers from category 1.

Initially, the cost of the service and the number of consumers in each category are known.
The ratio of payments by categories is also known (in which category they pay more, in which they pay less, and how many times). I do not yet know how to write these ratios mathematically.

The question is how to determine the amount of payment for each category (P1, P2, P3)?

Answer 1

I do not yet know how to write these ratios mathematically.

Until you know, there will be no solution. According to one equation, it is possible like this:
P1 = 0
P2 = 0
P3 = X / Q3