43 students prefer dogs.
SOLUTION:
Given, Mrs. Sprinkles surveyed her Algebra classes about if they prefer dogs or cats. The students who prefer dogs represent 5 less than 2 times the number of students who prefer cats. If 62 students were surveyed, we have to find number of students prefer dogs.
Now, let the number of students who like cats be n, then number of students who like dogs will be [tex]62-n[/tex].
So, now, according to given information, Students who like dogs are 5 less than twice that of those who like cats
[tex]62-\mathrm{n}=2 \times \mathrm{n}-5 \rightarrow 62-\mathrm{n}=2 \mathrm{n}-5 \rightarrow 2 \mathrm{n}+\mathrm{n}=62+5 \rightarrow 3 \mathrm{n}=67 \rightarrow \mathrm{n}=22.333[/tex]
Here, number of students can’t be in fractions, Now, let us see a condition where students who like dogs are 5 more than twice the students who prefers cats.
Then, [tex]62-n=2 \times n+5 \rightarrow 62-n=2 n+5 \rightarrow 2 n+n=62-5 \rightarrow 3 n=57 \rightarrow n=19[/tex]
This is a possible condition. So,19 students like cats, then [tex]62-19 = 43[/tex] students like dogs.
