Answered

The ratio of dogs to cats at the shelter is 3 to 2. If there are 48 dogs, how many cats are at the shelter?



Answer :

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].