TopCoder problem "Commission" used in TCCC '04 Qual. 3 (Division I Level One)

Problem Statement

*** You may only submit a given problem once - no resubmissions will be accepted. ***

Salesmen and saleswomen often work for a commission. In other words, they get to keep a certain percentage of the sales they make. You have a saleswoman working for you who gets a whopping 20% commission, which cuts deep into your profit margins. You are considering replacing her with a cheaper salesman who will keep commission% of his sales. Out of each sale, cost% of the sale goes towards the cost of your products and other overhead. Your current saleswoman sells $sales of products a year. Your task is to determine how much the potential salesman would have to sell in a year to make you the same profit.

Definition

Class:	Commission
Method:	equivalentSales
Parameters:	double, double, double
Returns:	double
Method signature:	double equivalentSales(double sales, double cost, double commission)
(be sure your method is public)

Notes

Your result must have relative or absolute error of less than 1e-9.

The commission is based on the gross sale, not the part of the sale that is above and beyond the cost. Therefore, if sales were $1000, your current saleswoman's commission would be $200.

Note that neither sales nor the return value need to be in whole cents.

Constraints

sales will be between 1 and 1e10, inclusive.

cost will be between 0.5 and 79.5, inclusive.

commission will be between 0.5 and 19.5, inclusive.

Examples

100.555

70.0

10.0

Returns: 50.2775

If you hire the new salesman, your profit margin will double from 10% to 20%. Thus, in order to make the same profits, he needs only sell half as much.

74.3

11.5

Returns: 303801.971830986

Your profit from your current saleswoman is $43139.88. If the potential salesman sells a little over $303801.97, your profit will also be the same.

10000000000

79.5

19.5

Returns: 5.0E9

Note that the exact answer is $5E9, but a return of $4.999999999999823E9, for example, has an error of $0.000177 which is a relative error of much less than 1e-9.

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=2293

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5002&pm=2293

Writer:

lars2520

Testers:

schveiguy , vorthys

Problem categories:

Math