To solve this problem, we need to determine how many cats were treated at the clinic, given the ratio of dogs to cats and the total number of animals treated.
1. Understand the ratio: The ratio of dogs to cats is 2 to 3. This means for every 2 dogs treated, 3 cats are treated.
2. Assign variables: Let's assume the number of dogs treated is [tex]\(2x\)[/tex] and the number of cats treated is [tex]\(3x\)[/tex]. This way, we are respecting the ratio given (2 dogs for every 3 cats).
3. Set up the equation: The total number of dogs and cats treated is given as 30. So, we can write the equation as:
[tex]\[
2x + 3x = 30
\][/tex]
4. Combine like terms: Simplify the equation by combining the terms on the left side.
[tex]\[
5x = 30
\][/tex]
5. Solve for [tex]\(x\)[/tex]: Divide both sides of the equation by 5 to find the value of [tex]\(x\)[/tex].
[tex]\[
x = \frac{30}{5} = 6
\][/tex]
6. Find the number of cats: We know [tex]\(3x\)[/tex] represents the number of cats treated. Substitute the value of [tex]\(x\)[/tex] we found into this expression.
[tex]\[
3x = 3 \times 6 = 18
\][/tex]
Therefore, the number of cats treated at the clinic is 18.
The correct answer is:
[tex]\[ \boxed{18} \][/tex]
