Sure, let's solve this step-by-step.
1. Understand the ratio: The ratio of dogs to cats is given as 3 to 2. This means for every 3 dogs, there are 2 cats.
2. Identify the number of dogs: The problem states there are 48 dogs.
3. Set up a proportion:
- Let's denote the number of cats as [tex]\( C \)[/tex].
- According to the ratio, the proportion can be set up as:
[tex]\[
\frac{3}{2} = \frac{48}{C}
\][/tex]
4. Solve the proportion:
- Cross multiply to find the value of [tex]\( C \)[/tex]:
[tex]\[
3 \times C = 2 \times 48
\][/tex]
- Simplify the equation:
[tex]\[
3C = 96
\][/tex]
5. Isolate [tex]\( C \)[/tex]:
- Divide both sides by 3 to solve for [tex]\( C \)[/tex]:
[tex]\[
C = \frac{96}{3}
\][/tex]
- Calculate the result:
[tex]\[
C = 32
\][/tex]
6. Result:
- Therefore, the number of cats at the shelter is [tex]\( 32 \)[/tex].
