Hello John!
I hope I can help you understand this problem!
So first, let us analyze what we know.
13% of the people surveyed answered yes.
The number of people who answered yes is 28.
We want to know how many people were surveyed in total.
Alright, first, let us think about how to work with percentages.
Suppose I am in a class of 100 people, and I tell you that 50% of the people are sick.
How many people are sick?
If it is something that we use in everyday life like "one half", then you might think to do:
100 / 2 = 50 people.
However, some percentages are much harder to write as fractions.
100 / 2 is actually 100 times 1/2.
1/2 is 50/100, which corresponds to 50%.
If we write 50% as a decimal, it becomes 0.5, or 1/2.
Let's say I told you 20% of the people in a room of 60 people are hungry.
How many people are hungry?
The first step is to convert the percentage into a decimal or fraction:
20% is 20/100, or 0.20.
We could work with 20/100 or 0.20, but I would recommend working with 0.20, unless you are required to write out the fractions in your class.
100% is written as 1, and 0% is written as 0.
Everything inbetween is written like so:
15% = 0.15 or 15/100
40% = 0.40 or 40/100
etc.
Okay, so we have 20 percent of the people are hungry, so we are working with 0.20 (20/100).
In order to figure out how many people are hungry we multiply the total number of people by the percentage.
so:
60 people total * 0.20 ("give us 20% of that number) = 12 people
So there are 12 people total who are hungry.
In terms of fractions:
60 people total * 20/100 ("give us 20% of that number)
= 1200/100 (cancel out the zeros on top and bottom)
= 12 / 1
= 12 people
The problem you are trying to solve is the reverse of this one.
If 12 people are hungry, and only 20% of the people in the room are hungry, how many people are in the room in total?
So we are solving the same equation above but in reverse:
X people total * 0.20 = 12 people.
To find X divide both sides by 0.20
(or multiply both sides by five to get rid of the 0.20. (because 0.20 * 5 = 1) )
X people total = 12 / 0.12 = 60
So there are 60 people total.
In terms of fractions:
X people total * 20/100 = 12 people.
Multiply both sides by 100 to get rid of it in the bottom of the fraction:
X * 20 = 12 * 100 = 1200
Divide both sides by 20:
X = 1200 / 20
X = 120 / 2
X = 60 * 2 / 2
X = 60, so the total number is 60 people.
So, getting back to your problem, we know that 13% of the people surveyed corresponds to 28 people.
First, convert 13% into a decimal => 0.13 (13/100).
Total number of people * 0.13 ("give me 13% of the total") = 28 ("this is 13% of the total sir")
X * 0.13 = 28.
Divide both sides by 0.13 to find the total number of people:
X = 28 / 0.13 = 215.38
You can't have a fraction of a person, so you either need to round up or round down.
I think you should round up, since you cannot have a fraction of a person.
So X is 216 people.
Doing the same thing with fractions yields:
Total number of people * 13/100 = 28
X * 13/100 = 28.
Multiply both sides by 100:
X * 13 = 28 * 100 = 2800
Divide both sides by 13:
X = 2800 / 13 = 215.38 people.
You can't have a fraction of a person, so let's round up to 216 people!
I hope this helps! Please let me know if you have any questions, or if something is confusing.
