To determine the number of dogs at the shelter, we can use the given ratio of cats to dogs.
The ratio of cats to dogs is [tex]\( 2 : 5 \)[/tex]. This means for every 2 cats, there are 5 dogs.
Let's break it down step-by-step:
1. Understand the ratio: The ratio [tex]\( 2 : 5 \)[/tex] indicates that there are 2 parts cats for every 5 parts dogs.
2. Define the parts:
- Let the number of parts of cats be [tex]\( 2x \)[/tex].
- Let the number of parts of dogs be [tex]\( 5x \)[/tex].
3. Relate the parts to the given number of cats:
- According to the problem, the number of cats is 14.
- Therefore, [tex]\( 2x = 14 \)[/tex].
4. Solve for [tex]\( x \)[/tex]:
- We have the equation [tex]\( 2x = 14 \)[/tex].
- Solving for [tex]\( x \)[/tex], we divide both sides of the equation by 2:
[tex]\[
x = \frac{14}{2} = 7
\][/tex]
5. Determine the number of dogs:
- The number of dogs is [tex]\( 5x \)[/tex].
- Substitute the value of [tex]\( x \)[/tex] we found:
[tex]\[
5x = 5 \times 7 = 35
\][/tex]
So, the number of dogs at the shelter is [tex]\( 35 \)[/tex].
