Final answer:
By using the given ratio of cats to dogs (5 to 7) and the total capacity of the shelter (60 animals), we solve for the number of cats and dogs that the shelter can hold when full, finding that there are 25 cats and 35 dogs.
Step-by-step explanation:
The question asks us to solve a ratio problem where the ratio of cats to dogs in terms of available space is 5 to 7 respectively and the total capacity is 60 animals. To find the number of cats and dogs when the shelter is full, we need to first find a common multiplier for both cats and dogs that will add up to the total capacity of 60.
Let c represent the number of cats and d represent the number of dogs. The ratio of cats to dogs can be written as c/5 = d/7. Since the total number of animals is 60, we can say that c + d = 60. We want to find values of c and d that fit both equations.
For every group of 5 cats and 7 dogs, there are 12 animals. To find how many groups of 12 fit into 60, we divide 60 by 12 which is 5. Therefore, we have 5 groups of cats and 5 groups of dogs. Multiplying these groups by the number of cats and dogs per group (5 cats * 5 groups and 7 dogs * 5 groups), we find there are 25 cats and 35 dogs when the shelter is completely full.