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
To represent the ratio of cats to dogs, we can divide the tape diagram into two parts, one for cats and one for dogs.
Let's first represent the number of dogs available for adoption, which we know is 25. We can divide the tape diagram as follows:
----------- --------------------
Dogs (25) Cats ( )
Next, we can determine the ratio of cats to dogs. The ratio given is 3:5, meaning that for every 3 cats, there are 5 dogs. Since we have 25 dogs, we can find the number of cats by multiplying 25 by 3/5.
(25 dogs) * (3/5) = 15 cats
Therefore, there are 15 cats available for adoption.
To solve this problem using a tape diagram, let's follow the steps below:
Step 1: Draw a tape diagram with two boxes, representing the cats and dogs available for adoption.
Step 2: Label one box "Cats" and the other box "Dogs".
Step 3: Write the given ratio of dogs to cats, which is 3:5.
Step 4: Since we know there are 25 dogs available for adoption, divide the tape diagram representing the dogs into five equal parts.
Step 5: Each part of the tape diagram representing the dogs will represent 5 dogs (25 dogs/5) available for adoption.
Step 6: Count the number of parts in the tape diagram representing the dogs. In this case, there are 5 parts in total.
Step 7: Multiply the number of parts by 3 (the ratio of dogs to cats) to find the number of cats available for adoption.
5 parts * 3 = 15 cats.
Answer: There are 15 cats available for adoption.
To solve this problem using a tape diagram, we'll start by understanding the given information.
We know that the ratio between cats and dogs available for adoption is 3:5. This means that for every 3 cats, there are 5 dogs. Since we are given that there are 25 dogs available, we can set up a tape diagram to represent this information.
First, draw a tape diagram with two sections: one for cats and one for dogs. Label the sections accordingly.
```
Cats:
Dogs:
```
Next, since we don't know the number of cats available, let's represent it with a variable, say "C". For dogs, we know that there are 25 available, so we can represent this number on the diagram.
```
Cats: C
Dogs: 25
```
Now, we'll use the ratio information to determine the relationship between the number of cats and the number of dogs. According to the ratio, for every 3 cats, there are 5 dogs. To represent this, we can divide the dog section of the tape diagram into groups of 3 and 5.
```
Cats: C
Dogs: [3][3][3][5][5]
```
Since we know that there are 25 dogs available, we can determine the number of groups of 5 dogs in the diagram. Divide 25 by 5.
```
Cats: C
Dogs: [3][3][3][5][5]
25 ÷ 5 = 5
```
We have determined that there are 5 groups of 5 dogs in the diagram. Each group of 5 dogs represents 3 cats. Therefore, we can multiply the number of groups by 3 to get the number of cats.
```
5 groups × 3 cats = 15 cats
```
Therefore, there are 15 cats available for adoption at the animal shelter.