Question

Results from a survey show that that \[36\% \] of dog owners say their dog sleeps in a family member's bed. If 12,500 pet owners were polled, how many people made this claim?

Answer 1

Hint: Here in this question, we have to find how many pet owners say their dog sleeps in a family member's bed. For finding this firstly, we have to convert the given survey percentage to decimal form and later by cross multiplying this into total numbers of pet owners we get the required result.

Complete step by step solution:
By given data, the results from a one survey shows that the \[36\% \] of dog owners says their opinions as the dog sleeps in a family member's bed.
The total number of pet owners were polled in survey is 12,500
Here, we have to find how many people made this claim, take this as \[x\].
Firstly, convert \[36\% \] in to decimal form
\[ \Rightarrow \dfrac{{36}}{{100}} = 0.36\]
Now multiply that by the total amount of pet owners to get the amount (the 36%) of the people who made the claim.
\[ \Rightarrow 0.36 \times 12,500\]
\[ \Rightarrow 0.36 \times 12,500\]
\[ \Rightarrow 4,500\]
Or
this can be solve also by
\[36\% \] can be written as \[\dfrac{{36}}{{100}}\]
To know the value of \[x\], by solving
\[ \Rightarrow \dfrac{x}{{12,500}} = \dfrac{{36}}{{100}}\]
On cross multiplying, we get
\[ \Rightarrow x \times 100 = 36 \times 1200\]
\[ \Rightarrow x \times 100 = 36 \times 12,500\]
\[ \Rightarrow x \times 100 = 4,50,000\]
Divide both side by 100, then
\[ \Rightarrow x = \dfrac{{4,50,000}}{{100}}\]
\[ \Rightarrow x = 4,500\]
Hence, \[36\% \] of 12,500 is 4,500
Therefore, 4500 people made that claim.
So, the correct answer is “4500”.

Note: This concept is somewhat related to the ratio and proportion concept. Since one of the terms is in the form of percentage so we will convert the percentage into the numeral form. While simplifying we use the simple arithmetic operations namely addition, subtraction, multiplication and division.