How to solve those 3 unknown values in this equation/example

[jackpotcity]

Hello!

I have a question to a problem that I am not sure how to start to solve.

If we assume we have 100 occurences and our goal is to get the TOTAL number to be 100.
1. In 43.125% of the occurences. What number to add here?
2. In 35% of the occurences. What number to add here?
3. In 21.875% of the occurences. What number to add here?

All the numbers that we added should be equal to 100 but I am not sure how to do this.
(The numbers should be equally balanced in the same way as the % of the occurences (43.125%, 35%, 21.875%))

 

[Dr.Peterson]

Hello!

I have a question to a problem that I am not sure how to start to solve.

If we assume we have 100 occurences and our goal is to get the TOTAL number to be 100.
1. In 43.125% of the occurences. What number to add here?
2. In 35% of the occurences. What number to add here?
3. In 21.875% of the occurences. What number to add here?

All the numbers that we added should be equal to 100 but I am not sure how to do this.
(The numbers should be equally balanced in the same way as the % of the occurences (43.125%, 35%, 21.875%))

I can't tell what you are asking for. Perhaps you could give a smaller example with actual (fake) numbers.

One problem is the incomplete sentences. What does "In 43.125% of the occurences" mean? And are you aware that 43.125% of 100 occurrences is 43.125 occurrences, which is not a whole number?

What you seem to be saying is that there are 100 numbers, and you want to somehow change some of them to make the sum of the new numbers 100. But that doesn't tell me much.

 

[jackpotcity]

I can't tell what you are asking for. Perhaps you could give a smaller example with actual (fake) numbers.

One problem is the incomplete sentences. What does "In 43.125% of the occurences" mean? And are you aware that 43.125% of 100 occurrences is 43.125 occurrences, which is not a whole number?

What you seem to be saying is that there are 100 numbers, and you want to somehow change some of them to make the sum of the new numbers 100. But that doesn't tell me much.

Yes, it is probably a bad example, also with the decimals. I will try to put this in another way/example. I try to figure this out but I am not sure if I am missing something.
The thing is that I have put this scenario in a C# code loop where I iterate 1 million times.

In each iteration/occurence, I do this using a random generator:
- With 43% chance I add the number 43
- With 35% chance I add the number 35
- With 22% chance I add the number 22

One iteration, perheps do this: 43 + 43 + 22 = 108
One iteration, perheps do this: 43 + 22 + 22 = 87
etc, etc 1 million times

This should give as I beleive an average of close to 100 in the end. But the code that I run shows an average of 106.75.
This leaves me wondering if I miss something mathematically when I do this and wonder if there is any type of clean
mathematical formula/equation to use to prove this?

 

[Harry_the_cat]

Hello!

I have a question to a problem that I am not sure how to start to solve.

If we assume we have 100 occurences and our goal is to get the TOTAL number to be 100.
1. In 43.125% of the occurences. What number to add here?
2. In 35% of the occurences. What number to add here?
3. In 21.875% of the occurences. What number to add here?

All the numbers that we added should be equal to 100 but I am not sure how to do this.
(The numbers should be equally balanced in the same way as the % of the occurences (43.125%, 35%, 21.875%))

I'm assuming the number of "occurences" must be a whole number. Is that correct?

43.125% of 100 = 43.125 which is rounded down to 43 (its closer to 43 thn it is to 44)
35% of 100 = 35
21.875% of 100 = 21.875 which is rounded up to 22

So if they are to be whole numbers the closest split you can get is 43, 35, 22 (adds to 100).

If they don't have to be whole numbers then the split is 43.125, 35, 22.875.

Does that answer your question? (Remember that "percent" means "per hundred".)

 

[jackpotcity]

If we assume we have 100 occurences and our goal is to get the TOTAL number to be 100.
1. In 43.125% of the occurences. What number to add here?
2. In 35% of the occurences. What number to add here?
3. In 21.875% of the occurences. What number to add here?

I think I found a solution for this problem. If we for example have 99 occurences and as you mentioned, let us use integers instead like:
43
35
22

If we now want the average result to be 100. We need to let those 3 numbers have the same probability like:

43 * 33 occurences = 141935 * 33 occurences = 115522 * 33 occurences = 726

(1419 + 1155 + 726) / 3 = 3300

3300 / 33 occurrences = 100

In that way I beleive we reach the result of 100 in this case.

Thank you for your help!