My math is a bit rusty, especially when I have to calculate percentages and when in background for that is finances.
I have the following table, that I just cannot figure at the moment:
+------+---------+----------+-----+ | id | input | output | % | +------+---------+----------+-----+ | 1 | 100 | x | Y | | 2 | 2000 | x | Y | | 3 | 1000 | x | Y | | 4 | 500 | x | Y | | 5 | 50 | x | Y | | 6 | 100 | x | Y | | 7 | 200 | x | Y | | 8 | 4000 | x | Y | | 9 | 600 | x | Y | | 10 | 250 | x | Y | +------+---------+----------+-----+ | n | z | x | Y | +------+---------+----------+-----+
For each row:
- $\text{output} = \text{input} \times (Y / 100)$; (fixed from
input * Y
) id
($n$) can fill up to infinity;- $z > 0$
Ending half of the table (> id / 2 < n
), $Y = 50$.
I have to find the $Y$ of first half, where, for $\text{id} / 2$, $Y = 100$.
$Y$ has to follow up, so that in the end totals of input
match the totals of output
. For first half, each rows output has to be higher than input.
How do I do this, and, how would this break into steps?
P.S. The tag might be wrong, I have no idea about the English mathematical terminology, not my native language.
update
To narrow it down a bit (previous table with limit of 10, filled in, explained):
+------+---------+----------+-----+ | id | input | output | % | +------+---------+----------+-----+ | 1 | 100 | x | Y | // highest Y | 2 | 2000 | x | Y | // Y higher than that of id 3 | 3 | 1000 | x | Y | // Y higher than that of id 4 | 4 | 500 | x | Y | // lowest Y, but above 100 | 5 | 50 | 50 | 100 | | 6 | 100 | 50 | 50 | | 7 | 200 | 100 | 50 | | 8 | 4000 | 2000 | 50 | | 9 | 600 | 300 | 50 | | 10 | 250 | 125 | 50 | +------+---------+----------+-----+ | Totals: 8800 | 2625 | +----------------+----------+
Now, here the last half has recieved 50% of their input, that totals $2625$ of total input.
That leaves us with $6175 (8800 - 2625)$. Now, this $6175$ has to be distributed, that everyone recieves more than their input, and the closer to first, the more they recieve.
The first row, does not have to have the highest output, but the highest % ($Y$).
I'd call it input increase percentage
that, when applied, results in higher output
.
Thanks in advance!