# Needing help getting a percentage formula rigth

#### thejnc93

##### New member
I need a formula to find how many more winning matches are needed to get 1% and 5% better rate.

Example:
Over a=200 matches, b=150 are won. Thats c=75%

Being a 100/a*b=c

1% of that would be 100/a = 0.5

And the amount of matches it represents 1/(100/a) = 2 matches

But adding that to the total and won matches change the whole percentage.
In this case, by trial and error I find that with 9 more winning matches I can get to 76%
But I need a simpler and smarter way to find that number with several changing values.

I know there has to be a way. I just cant find it

#### tkhunny

##### Moderator
Staff member
I need a formula to find how many more winning matches are needed to get 1% and 5% better rate.

Example:
Over a=200 matches, b=150 are won. Thats c=75%

Being a 100/a*b=c

1% of that would be 100/a = 0.5

And the amount of matches it represents 1/(100/a) = 2 matches

But adding that to the total and won matches change the whole percentage.
In this case, by trial and error I find that with 9 more winning matches I can get to 76%
But I need a simpler and smarter way to find that number with several changing values.

I know there has to be a way. I just cant find it
I can't tell what it is you are trying to do.

150/200 = 0.75 = 75% No "100/" in there.
15/200 = 0.075 = 7.5%

#### thejnc93

##### New member
I can't tell what it is you are trying to do.

150/200 = 0.75 = 75% No "100/" in there.
15/200 = 0.075 = 7.5%
I just need to know how many more wins I need to get 1% more
Tried adding 2 matches won but it changes the total and win amounts

To get 76% Its 9 more winning matches

How I figure that out that if "a" and "b" are different in every case?

#### Dr.Peterson

##### Elite Member
I need a formula to find how many more winning matches are needed to get 1% and 5% better rate.

Example:
Over a=200 matches, b=150 are won. Thats c=75%

Being a 100/a*b=c

1% of that would be 100/a = 0.5

And the amount of matches it represents 1/(100/a) = 2 matches

But adding that to the total and won matches change the whole percentage.
In this case, by trial and error I find that with 9 more winning matches I can get to 76%
But I need a simpler and smarter way to find that number with several changing values.

I know there has to be a way. I just cant find it
Your calculation methods are rather awkward and hard to understand; they certainly aren't helping you to think clearly. (Your 0.5 is not 1% of anything in the problem, though 2 is 1% of the total number of matches.)

Here is what I think you are trying to do:

Given 150 out of 200 matches won, you have a winning rate of 150/200 = 0.75, which as a percentage is 0.75 * 100% = 75%.

You want to know how many more matches, if all are won, would increase the rate to 76%. Since playing more matches increases both the numerator and the denominator, you need algebra to solve this.

If you play 200+x matches, out of which you win 150+x, then your new rate is (150+x)/(200+x), and you want this to equal 0.76. To solve the equation, we can multiply by the denominator:

$$\displaystyle \dfrac{150+x}{200+x} = 0.76$$

$$\displaystyle 150+x = 0.76(200+x)$$

$$\displaystyle 150+x = 152 + 0.76x$$

$$\displaystyle x - 0.76x = 152 - 150$$

$$\displaystyle 0.24x = 2$$

$$\displaystyle x = 2/0.24 = 8.33$$

So you can't get exactly 76%, but 9 is the first number at which you will be over 76%, as you found.

#### thejnc93

##### New member
Your calculation methods are rather awkward and hard to understand; they certainly aren't helping you to think clearly. (Your 0.5 is not 1% of anything in the problem, though 2 is 1% of the total number of matches.)

Here is what I think you are trying to do:

Given 150 out of 200 matches won, you have a winning rate of 150/200 = 0.75, which as a percentage is 0.75 * 100% = 75%.

You want to know how many more matches, if all are won, would increase the rate to 76%. Since playing more matches increases both the numerator and the denominator, you need algebra to solve this.

If you play 200+x matches, out of which you win 150+x, then your new rate is (150+x)/(200+x), and you want this to equal 0.76. To solve the equation, we can multiply by the denominator:

$$\displaystyle \dfrac{150+x}{200+x} = 0.76$$

$$\displaystyle 150+x = 0.76(200+x)$$

$$\displaystyle 150+x = 152 + 0.76x$$

$$\displaystyle x - 0.76x = 152 - 150$$

$$\displaystyle 0.24x = 2$$

$$\displaystyle x = 2/0.24 = 8.33$$

So you can't get exactly 76%, but 9 is the first number at which you will be over 76%, as you found.
Exactly that's what I've wanted. Thanks Dr.