To determine how many dogs are necessary to make the cat-to-dog ratio 3:2 in an area with 1425 cats, follow these steps:
1. Understand the given ratio:
- The ratio of cats to dogs is 3:2. This means for every 3 cats, there should be 2 dogs.
2. Set up the ratio equation:
- Let's denote the number of cats as [tex]\( C \)[/tex] and the number of dogs as [tex]\( D \)[/tex].
- We are given that [tex]\( C = 1425 \)[/tex] and we need to find [tex]\( D \)[/tex] such that the ratio [tex]\( \frac{C}{D} = \frac{3}{2} \)[/tex].
3. Convert the ratio into a usable form:
- Since the ratio of cats to dogs is 3:2, we can set up the equation: [tex]\( \frac{C}{D} = \frac{3}{2} \)[/tex].
4. Solve for [tex]\( D \)[/tex]:
- Rearrange the equation to solve for [tex]\( D \)[/tex]:
[tex]\[
\frac{C}{D} = \frac{3}{2}
\][/tex]
Multiply both sides by [tex]\( 2D \)[/tex] to eliminate the fraction:
[tex]\[
2C = 3D
\][/tex]
Now, plug in the value of [tex]\( C \)[/tex] (which is 1425):
[tex]\[
2 \cdot 1425 = 3D
\][/tex]
[tex]\[
2850 = 3D
\][/tex]
Finally, solve for [tex]\( D \)[/tex] by dividing both sides by 3:
[tex]\[
D = \frac{2850}{3}
\][/tex]
[tex]\[
D = 950
\][/tex]
5. Conclusion:
- Therefore, in order to achieve a cat-to-dog ratio of 3:2 with 1425 cats, you would need 950 dogs.
The number of dogs necessary is [tex]\( \boxed{950} \)[/tex].
