I need help to figure out an equation

[madx]

I need to help to figure out an equation.

Current # of Surveys 11
my current % 55% how many surveys are at 100
that means I have 6 @100 and 5@0
if my goal is to be at 75%
??? how many mory@100 do I need

I know the answer is 9 but I need an equation to figure 9 out by it self.

 

[Deleted member 4993]

I need to help to figure out an equation.

Current # of Surveys 11
my current % 55% how many surveys are at 100
that means I have 6 @100 and 5@0
if my goal is to be at 75%
??? how many mory@100 do I need

I know the answer is 9 but I need an equation to figure 9 out by it self.

If you add 'x' more people to your survey - how many total surveys would you have?

 

[Dr.Peterson]

I need to help to figure out an equation.

Current # of Surveys 11
my current % 55% how many surveys are at 100
that means I have 6 @100 and 5@0
if my goal is to be at 75%
??? how many mory@100 do I need

I know the answer is 9 but I need an equation to figure 9 out by it self.

If this is an exercise you were assigned, please copy it exactly as given; what you have written is not at all clear. If it is a real situation, you'll have to explain in more detail. Maybe we need to know what sort of "surveys" these are, in order to make sense of it.

Here is how I read it: You have given 11 surveys, which are 55% of something -- maybe of the total number of surveys you are supposed to give? From that you could work out the total number you are supposed to give. But that doesn't seem to be what you mean.

Apparently a survey can be either "at 100" or "at 0", but I don't know what that would mean. Maybe those are percentages (percent of answers that are favorable?), but why would they all be either 100% or 0%?

Anyway, having "6@100 and 5@0" would mean that there are 6 "at 100" out of 11 in all, so 6/11 = 54.5% are "at 100", which seems to fit what you said about 55% (rounded).

Then, what is the goal? It sounds like you need to do more surveys until 75% of them are "at 100", and you are assuming that they will all be "at 100". (How could you expect that?) Let's suppose that's true.

If you need to solve this with an equation (there are other ways), then we can let x = the number of additional surveys, all of which are 100. Then, just as we calculated the percentage above, you want the new number of "100" surveys, over the new total number of surveys, to equal 0.75. That will be an equation; then you can solve it.

Is that what you want to do?

By the way, we can also check your claimed answer of 9, which can help us see both whether I have interpreted the question correctly, and what the equation should look like. If you have 9 more surveys "at 100", then you will have 6+9 = 15 "at 100", out of 11+9 = 20 total, for a percentage of 15/20 = 0.75 = 75%, so it looks like we have it right. Replace the 9's in my work with x, and you will have your equation.

 

[madx]

I need to help to figure out an equation.

so I apologize for not explaining more clearly.
this is a real-world problem.
I work for a restaurant were we receive surveys and although you can rate us on a 1 to 5 scale in the end 1-4 all=0 and 5=100.
if our goal is to have 75% at 100 (5)
when I run the report I get the number of surveys and at what percentage is 100
so in this example, we had

Current # of Surveys 11
my current % is 55% this is how many of the total number of surveys are at 100....6 @100 and 5@0
if my goal is to be at 75% of the total number of surveys
X = how many more surveys at 100 do I need to get to reach 75% of the total number of surveys. in this example, x would equal 9. I need an equation that would solve for x.

 

[Dr.Peterson]

so I apologize for not explaining more clearly.
this is a real-world problem.
I work for a restaurant were we receive surveys and although you can rate us on a 1 to 5 scale in the end 1-4 all=0 and 5=100.
if our goal is to have 75% at 100 (5)
when I run the report I get the number of surveys and at what percentage is 100
so in this example, we had

Current # of Surveys 11
my current % is 55% this is how many of the total number of surveys are at 100....6 @100 and 5@0
if my goal is to be at 75% of the total number of surveys
X = how many more surveys at 100 do I need to get to reach 75% of the total number of surveys. in this example, x would equal 9. I need an equation that would solve for x.

Okay, what I said is correct, then. (I won't bother to discuss whether this is a good way to handle surveys.) Essentially, each person just says Yes or No, and your goal is to have 75% of customers say Yes. You want to find the least number of additional surveys it will take to reach the goal (by assuming that they are all "Yes").

Here is what I said:

If you have 9 more surveys "at 100", then you will have 6+9 = 15 "at 100", out of 11+9 = 20 total, for a percentage of 15/20 = 0.75 = 75%, so it looks like we have it right. Replace the 9's in my work with x, and you will have your equation.
​

So we can do what I said to do:

If you have x more surveys "at 100", then you will have 6+x "at 100", out of 11+x total, for a percentage of (6 + x)/(11 + x) = 0.75.
​

So that's the equation. To solve it, we can multiply both sides by the denominator (or cross-multiply, if that is more familiar to you), and get

6 + x = 0.75(11 + x)
​

Distributing,

6 + x = 8.25 + 0.75x
​

Subtracting 0.75x from each side,

6 + 0.25x = 8.25
​

Subtracting 6 from each side,

0.25x = 2.25

​

Dividing by 0.25,

x = 2.25/0.25 = 9
​

And there's the answer.

Now, to make this
more general, we could replace the numbers you gave for this example with variables:

y = current number of Yes surveys
t = current total number of surveys
g = goal percentage, as a decimal

y + x = g(t + x)
​

Then you could solve this equation for x, doing just what I did above. The result is

x = (gt - y)/(1 - g)
​

 

[Dr.Peterson]

Perhaps I should add that if what you know is

c = current percent of Yes, as a decimal (like your 55% = 0.55)
​

then y = ct and the formula becomes

x = (gt - ct)/(1 - g) = (g - c)/(1 - g) * t
​

In the example, this would be

x = (0.75 - 0.55)/(1 - 0.75) * 11 = 0.20/0.25 * 11 = 8.8
​

This is not the same as your answer of 9, because we neglected to consider that your 55% was a rounded number. (It was really 6/11 = 0.5454... = 54.54...%, and if you used the exact percentage in the formula, you would get 9.)

This is a reason not to use this new formula with the percent, but to use the formula I gave before that uses the actual number y of Yes surveys.