An animal shelter has cats and dogs available for adoption in a ratio of 3:5 . If there are 25 dogs available for adoption, how many cats are available? Use a tape diagram to help organize your thinking.(1 point)
First, let's represent the ratio of cats to dogs as 3:5 using a tape diagram.
We will divide the tape diagram into 3 equal parts for cats and 5 equal parts for dogs.
Thus, each part of the tape diagram represents 1 cat or 1 dog.
There are 25 dogs available for adoption, so we will draw 25 parts of the tape diagram to represent the dogs.
Since there are 5 parts in the tape diagram for dogs, each part represents 25 / 5 = <<25/5=5>>5 dogs.
Now, we need to determine the number of parts in the tape diagram for cats.
Since the ratio of cats to dogs is 3:5, we have 3 parts for cats.
If 5 parts represent 25 dogs, then 1 part represents 25 / 5 = <<25/5=5>>5 dogs.
So, if 1 part represents 5 dogs, then 3 parts represent 3 * 5 = <<3*5=15>>15 dogs.
Therefore, there are 15 cats available for adoption.
To determine the number of cats available for adoption, we need to find the total number of cats and dogs combined.
Since the ratio of cats to dogs is 3:5, we can consider the ratio as 3x:5x, where x is a common factor for both the number of cats and dogs.
Given that there are 25 dogs available for adoption, we can set up an equation:
5x = 25
To find x, we divide both sides of the equation by 5:
x = 25 / 5
x = 5
Now, knowing the value of x, we can find the number of cats:
3x = 3 * 5 = 15
Therefore, there are 15 cats available for adoption.
To illustrate this process using a tape diagram, we can draw a rectangle divided into two parts representing cats and dogs. Since the ratio is 3:5, we divide the rectangle into three equal parts for cats and five equal parts for dogs. Then we label one part of the dog section as 25, representing the 25 dogs available. Finally, we count the number of parts in the cat section, which would be 15.