Step 1 :The question is asking for the equation that can be used to find the number of dogs in the shelter. Given that there are 50 animals in total and 60% of them are dogs, we can represent this situation with the equation \(\frac{60}{100} = \frac{x}{50}\), where x is the number of dogs.
Step 2 :Looking at the provided options, the equation that matches this format is \(\frac{60 \times 2}{50 \times 2}=\frac{120}{100}\), because it can be simplified to \(\frac{60}{100} = \frac{x}{50}\).
Step 3 :Final Answer: The equation that can be used to find the number of dogs in the shelter is \(\boxed{\frac{60 \times 2}{50 \times 2}=\frac{120}{100}}\).