Anyone good at Math? I need to figure out how many possiblities there are to break up $10,000?

Question

I am publishing a directory and I need to bring in $10,000 per month from my advertisers. I have different size ads that are priced at different levels. Here are the prices.

100

250

300

400

Are there infinite possibilities? Is there a way to figure out how many combinations there could be.

Obviously this is my first time doing something like this.

Answer 1

what math man said.

there is no easy way to do this because you dont have a "yes/no" situation. you have a value plugged to each that must add up to a predetermined sum. ( 10 000$)

if you were to say "I have 20 add spaces available and 200 different companys want to advertise how many combinations are there " it would be easy ( 200C20 )

so for 10 000$ you would have to start like this.

how can I sum 400,300,250,and 100 to make 10000?

400 , 300 , 250 , 100

-------------------------------

25......0......0........0

24  .....1......0.......1

24.......0.......0......4

23.......2.......0......2

23.......1......0.......5

23.......1.......2......0

23.......0.......0.......8

23.......0......2........3

22......4.......0......0

22......3.......0......3

22.....2.......2......1

22.....2.......0.....6

22.....1......2.......4

22.....1......0......9

22.....0.......4.....2

22.....0......2......7

22....0.......0......12

looks like a pattern but it doesnt match up with the previous post. you would have to repeat this method down to 0,0,0,100 and then count them all if you were to do it by hand.

Answer 2

It's not infinite, but there many combinations.

a * 100 + b * 250 + c * 300 + d * 400 = 10000

You could have:

0-100 of the a's

0-40 of the b's

0-33 of the c's

0-25 of the d's

A total of 3352 different combinations,

found by computer program.

I don't know any better way to figure it out,

because there are so many combinations,

and there just isn't a simple formula.

Here are the number of combinations for each number of $400 ads:

Subtotal: 0 -> 364  (combinations with 0 $400 ads)

Subtotal: 1 -> 337 (combinations with 1 $400 ads)

Subtotal: 2 -> 310

Subtotal: 3 -> 285

Subtotal: 4 -> 261

Subtotal: 5 -> 238

Subtotal: 6 -> 216

Subtotal: 7 -> 195

Subtotal: 8 -> 175

Subtotal: 9 -> 156

Subtotal: 10 -> 139

Subtotal: 11 -> 122

Subtotal: 12 -> 106

Subtotal: 13 -> 92

Subtotal: 14 -> 78

Subtotal: 15 -> 66

Subtotal: 16 -> 55

Subtotal: 17 -> 44

Subtotal: 18 -> 35

Subtotal: 19 -> 27

Subtotal: 20 -> 20

Subtotal: 21 -> 14

Subtotal: 22 -> 9

Subtotal: 23 -> 5

Subtotal: 24 -> 2

Subtotal: 25 -> 1

A few examples, selected at random,

just to give you an idea of the variety:

D C B A

0 1 10 72 = 1 x 300 + 10 x 250 + 72 x 100 = 300 + 2500 + 7200

0 1 12 67

0 1 14 62

0 1 16 57

0 1 18 52

0 1 20 47

0 1 22 42

0 1 24 37

0 1 26 32

0 1 28 27

0 1 30 22

0 1 32 17

0 1 34 12

0 2 8 74

4 20 8 4

6 19 4 9

9 3 18 10

Here's one that has about the same number of each:

9 10 10 9

9 x $100 + 10 x $250 + 10 x $300 + 9 x $400 =

900 + 2500 + 3000 + 3600 = 10000.

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