To determine how much medicine each sick dog receives, we need to start by understanding the total amount of medicine available and then divide it equally among the dogs.
1. Convert the mixed fraction to an improper fraction:
[tex]\[
5 \frac{1}{2} \text{ bottles of medicine can be written as } 5 + \frac{1}{2}
\][/tex]
[tex]\[
5 = \frac{10}{2} \implies 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2}
\][/tex]
So, the total amount of medicine is [tex]\(\frac{11}{2}\)[/tex] bottles.
2. The number of sick dogs is 3.
3. To find the amount of medicine given to each dog, we need to divide the total amount of medicine by the number of dogs.
[tex]\[
\frac{11}{2} \div 3 = \frac{11}{2} \times \frac{1}{3} = \frac{11}{6}
\][/tex]
4. Now, convert [tex]\(\frac{11}{6}\)[/tex] back to a mixed number:
[tex]\[
\frac{11}{6} = 1 \frac{5}{6}
\][/tex]
Therefore, each dog receives [tex]\(1 \frac{5}{6}\)[/tex] bottles of medicine. So the correct answer is:
C. [tex]\(1 \frac{5}{6}\)[/tex]
