Need to determine the formula to work out a reduction percentage

We currently calculate a value for a business function as follows;

Inputs: A list of values such as;

• 12
• 12
• 6
• 12

We then add 1 to each of these values and we have values as follows;

• 13
• 13
• 7
• 13

For each of these we calculate another value using y = 100/x so 7,692307692 = 100/13

• 7,692307692
• 7,692307692
• 14,28571429
• 7,692307692

The final step is to sum these values for the total (Final percentage) we are looking for, i.e. 37,36263736

So now to the question :)

In some cases we want the final percentage to be larger than the one we have calculated. For example we may need it to be 90.

We need a formula to reduce the initial list of values by to arrive at 90. So if we have a reducer of 0.349 = 34.9% we would have a new final percentage of 90,14637229.

Original   +1   /100         |   (Original*0.349)  +1       /100
12         13   7,692307692  |   4,188             5,188    19,27525058
12         13   7,692307692  |   4,188             5,188    19,27525058
6          7    14,28571429  |   2,094             3,094    32,32062056
12         13   7,692307692  |   4,188             5,188    19,27525058
37,36263736                                 90,14637229


A. So we have the values 12, 12, 6, 12 and we calculate 37,36263736.

B. We know we want it to be roughly 90

C. We need to determine the reducer, in this case it is 0.349

Can anyone help determine a formula to work back from 90 to get 0.349?

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