Problem Statement
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.
756840
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.
1e10
0.5
19.5
Returns: 9.9375E9
1e10
79.5
0.5
Returns: 2.5E8
8.43721326924896E9
68.23599520710148
6.251860358028325
Returns: 3.8905164397896976E9
9.614646660519178E9
9.895342436486649
4.655836078244928
Returns: 7.888131164524941E9
7.944156667578871E9
72.41836889584326
2.9313429527628
Returns: 2.443365567059476E9
7.260833675727328E9
11.418929884569774
4.633100706928474
Returns: 5.931718741026545E9
2.0746127364318938E9
22.64220742995874
11.691988834512387
Returns: 1.8121335646584523E9
1.8306452010679398E9
36.66797096334943
18.410595141000577
Returns: 1.7658735291653848E9
5.264633569918279E8
59.87190051072578
14.298778074889587
Returns: 4.1025881621061015E8
3.6735972854196725E9
17.029134770671543
18.06905144637416
Returns: 3.5643009968967166E9
4.573054142666119E9
18.358345872989382
13.682065099354112
Returns: 4.1479153390936646E9
7.984716708616845E9
64.3895524692775
11.721898514122941
Returns: 5.2177719601526985E9
2.4042298818893364E8
20.494151393102438
11.662931514081114
Returns: 2.1087793022248238E8
2.47817639550108E9
31.318728727639993
4.746916867369422
Returns: 1.8869476120139008E9
4.996936228037295E9
76.350585393411
2.859257098792855
Returns: 8.771406398414612E8
9.091314478993944E9
73.72019169441944
14.910274517646714
Returns: 5.021464665017376E9
6.534539845041672E9
19.66943408579149
18.430553580116193
Returns: 6.368859584591379E9
4.542526576450711E9
1.0335515680986662
8.7088215601534
Returns: 3.9742590524736853E9
5.731609554464256E9
55.296680125977076
9.85548832088176
Returns: 4.0630873688946567E9
4.131705055736418E9
27.219588754580133
1.2474141949261388
Returns: 3.0485664096055565E9
9.946869642678268E9
48.44162556727712
0.8045216547176959
Returns: 6.184890790264513E9
7.646103454373939E9
35.75761594507076
9.255852306502309
Returns: 6.152085516137515E9
1.2399359640902324E9
21.754973004989843
8.584996713113714
Returns: 1.0367509662034758E9
8.752555831912825E9
6.513563246227915
5.937716571674271
Returns: 7.346699520425918E9
5.003354990872392E9
60.52583214236826
3.0768994063626303
Returns: 2.677018883272023E9
3.422359995200295E9
71.2152718023831
12.874485296845062
Returns: 1.8896318893266916E9
2.598964065327838E9
19.98726881332888
6.039423486389426
Returns: 2.1084758362879527E9
5.320123952779625E9
54.592690939724044
14.717027072856984
Returns: 4.404326866812755E9
9.121112259343814E8
58.43234952883726
12.412208453095609
Returns: 6.747315338106012E8
8.73347408388608E9
21.527597653311037
2.057687306151056
Returns: 6.6828386423538885E9
7.983649183488454E9
69.92054026418022
0.5369999195981824
Returns: 2.723905557982557E9
2.5365280222381577E9
41.410442425386705
4.255115000398136
Returns: 1.801499923737706E9
6.983296107663028E9
50.59368809971328
2.1275415178144668
Returns: 4.343450173783032E9
2.344918918375332E9
42.75005208440239
16.78683145431353
Returns: 2.1587093435908976E9
7.399319145857055E9
30.02059818057305
14.375326462116877
Returns: 6.650835256310949E9
5.881222812389608E9
75.93162131485185
2.527945332233495
Returns: 1.1107966650678055E9
8.307698682448638E9
4.501645030260655
1.619685089469148
Returns: 6.681151159353621E9
7.54288708241172E9
67.20499050675615
5.435686958195973
Returns: 3.527547573675895E9
1.5368430181622431E9
68.54515564435899
15.871411208255633
Returns: 1.1296803089283156E9
9.134943958952156E9
7.921538377594148
19.086530927436954
Returns: 9.020623256558752E9
4.268211084728977E9
33.883890100775695
16.764238716239326
Returns: 3.9883653190501714E9
2.0504570675327318E9
57.965372527093386
12.134115797400105
Returns: 1.511046303240458E9
9.634234193425398E9
45.744310960784944
6.8380776872198386
Returns: 6.960015936084612E9
2.175023147234453E9
61.06222966380364
1.6911366382143893
Returns: 1.1058741354247205E9
7.936850206636174E9
32.87821242653537
5.817766067939422
Returns: 6.10071835835127E9
8.248795056362733E9
49.34506157148808
5.186719627461921
Returns: 5.561385759768835E9
9.67568196780663E9
75.08329950457731
2.6425198581110316
Returns: 2.1357656696461496E9
1.100120128750106E9
27.43423717733566
18.10287486660254
Returns: 1.0617992533001661E9
8.326025367840853E9
72.99754913143863
9.591320108702227
Returns: 3.3485811101434083E9
9.297565596786016E9
40.406362214946704
2.980545136155373
Returns: 6.502461308816779E9
6.143766427041953E9
51.4754788380603
11.120716840795613
Returns: 4.685298692013166E9
3.549056262864414E9
60.01081400760803
12.929190463929928
Returns: 2.6216835720184016E9
9.81625034316587E9
51.420138041621264
16.93223413009082
Returns: 8.864711165043602E9
2.7412011268608195E8
7.306957997395385
8.93608724200775
Returns: 2.3791009262698826E8
5.862888236790677E9
72.832805442443
17.780603413441227
Returns: 4.476647594119693E9
4.822574642830569E9
41.576085066556196
17.30550386322547
Returns: 4.506550545444533E9
3.8735230133727393E9
65.78657777418557
3.3508835264591132
Returns: 1.783910864456067E9
7.913921699080601E9
12.776200986665586
14.457174701425274
Returns: 7.311097453495468E9
1.2316974075493464E9
5.9666997868706115
15.917311076296672
Returns: 1.1673234244669924E9
9.098493722151285E9
11.399584936008234
7.862255956803612
Returns: 7.7306747230645275E9
7.3981094289717045E9
20.239306056906333
18.960172302662695
Returns: 7.271584871539923E9
7.93505695834775E9
12.134743969507358
4.517965059878404
Returns: 6.4610938858789835E9