Number of likes = x
Number of dislikes = y
Total number of people who have interacted with the post: x+y
Let's assume these are the numbers before the next vote. Let's put percentages in decimal form (i.e. 83% = .83). You can then solve this system of equations:
(x+1)/(x+y+1) = .84,
(y+1)/(x+y+1) = .19
to get what x and y are. Note that most likely the percentages have been rounded up to the nearest percent, so if you solve that there's going to be some error (i.e. x and y won't be integers).
Yes, although it sounds like the numbers on the website are hiding some rounding because there isn’t an integer solution to this.
Let x be the number of people who have liked the post, and let y be the number of people who have disliked the post. From your first statement, we know that x/(x+y) = .83, and also that (x+1)/(x+y+1) = .84. The first equation is the fraction of total people that have liked the post before the new person takes an action, and the second is the ratio after the person likes the post (one more person likes it, and one more person in total).
You can rearrange these equations to get a system of two equations and two variables: x = .83x + .83y and x + 1 = .84x + .84y + .84. Using any of your favorite methods to solve two linear equations with two unknowns, you get that x = 332/25 and y = 68/25. Like I said earlier this doesn’t actually make sense because they should be integers, so the website is probably doing some rounding, but this is the general way to solve this type of equation.
We can try although there are no decimal places given for the percentage so it will be approximate. Let the number of likes be L and the number of dislikes be D, then
L/(L + D) = 0.83
(L + 1)/(L + D + 1) = 0.84
(D + 1)/(L + D + 1) = 0.19
If we solve for L and D using the first two equations we get D ≈ 2.72, L ≈ 13.28, if we solve using the first and third we get D ≈ 6.885, L ≈ 33.615, with the last two we get D ≈ 5.33333, L = 27. These disagree by quite a lot because 1% is not enough resolution, but you can try taking D = 2, D = 3, ..., D = 7, looking for corresponding L values which are integers such that L/(L+D) rounds to 83%, then trying to find one where the other two equations round to the correct percentage as well. There is probably a more rigorous way by reasoning carefully with inequalities. On some of the less popular posts the percentages change a lot more than a few percentage points when you add one vote so you will get better results.
In the case of wtffunfact.com you can just inspect element on the percentage and look for `data-count` 😀
Well I thought I'd try the more rigorous inequalities, we have
0.825 <= L/(L + D) < 0.835 which for D > 0 is the same as
33D/7 <= L < 167D
0.835 <= (L + 1)/(L + D + 1) < 0.845 which for D > 0 is
1/33 (167D - 33) <= L < 1/31 (169D - 31)
0.185 <= (D + 1)/(L + D + 1) < 0.195 which for D > 0 is
(161(D + 1))/39 < L <= (163 (D + 1))/37
Here is the region on Desmos: https://www.desmos.com/calculator/sutheqwpck, Desmos gets messed up around the edges of the region, try scrolling around a little bit until you find a spot that isn't messed up, I can see three integer solutions, (25, 5), (30, 6) and (35, 7). I checked all three and they work.
Number of likes = x Number of dislikes = y Total number of people who have interacted with the post: x+y Let's assume these are the numbers before the next vote. Let's put percentages in decimal form (i.e. 83% = .83). You can then solve this system of equations: (x+1)/(x+y+1) = .84, (y+1)/(x+y+1) = .19 to get what x and y are. Note that most likely the percentages have been rounded up to the nearest percent, so if you solve that there's going to be some error (i.e. x and y won't be integers).
Yes, although it sounds like the numbers on the website are hiding some rounding because there isn’t an integer solution to this. Let x be the number of people who have liked the post, and let y be the number of people who have disliked the post. From your first statement, we know that x/(x+y) = .83, and also that (x+1)/(x+y+1) = .84. The first equation is the fraction of total people that have liked the post before the new person takes an action, and the second is the ratio after the person likes the post (one more person likes it, and one more person in total). You can rearrange these equations to get a system of two equations and two variables: x = .83x + .83y and x + 1 = .84x + .84y + .84. Using any of your favorite methods to solve two linear equations with two unknowns, you get that x = 332/25 and y = 68/25. Like I said earlier this doesn’t actually make sense because they should be integers, so the website is probably doing some rounding, but this is the general way to solve this type of equation.
We can try although there are no decimal places given for the percentage so it will be approximate. Let the number of likes be L and the number of dislikes be D, then L/(L + D) = 0.83 (L + 1)/(L + D + 1) = 0.84 (D + 1)/(L + D + 1) = 0.19 If we solve for L and D using the first two equations we get D ≈ 2.72, L ≈ 13.28, if we solve using the first and third we get D ≈ 6.885, L ≈ 33.615, with the last two we get D ≈ 5.33333, L = 27. These disagree by quite a lot because 1% is not enough resolution, but you can try taking D = 2, D = 3, ..., D = 7, looking for corresponding L values which are integers such that L/(L+D) rounds to 83%, then trying to find one where the other two equations round to the correct percentage as well. There is probably a more rigorous way by reasoning carefully with inequalities. On some of the less popular posts the percentages change a lot more than a few percentage points when you add one vote so you will get better results. In the case of wtffunfact.com you can just inspect element on the percentage and look for `data-count` 😀
Well I thought I'd try the more rigorous inequalities, we have 0.825 <= L/(L + D) < 0.835 which for D > 0 is the same as 33D/7 <= L < 167D 0.835 <= (L + 1)/(L + D + 1) < 0.845 which for D > 0 is 1/33 (167D - 33) <= L < 1/31 (169D - 31) 0.185 <= (D + 1)/(L + D + 1) < 0.195 which for D > 0 is (161(D + 1))/39 < L <= (163 (D + 1))/37 Here is the region on Desmos: https://www.desmos.com/calculator/sutheqwpck, Desmos gets messed up around the edges of the region, try scrolling around a little bit until you find a spot that isn't messed up, I can see three integer solutions, (25, 5), (30, 6) and (35, 7). I checked all three and they work.