Question

2. At the kennel, the ratio of cats to dogs is 4 : 5. There are 27 animals in all. Here is a tape diagram representing this ratio. number of cats number of dogs a. What is the value of each small rectangle? b. How many dogs are at the kennel?

Answer 1

The ratio of cats to dogs is 4:5, and we can express this ratio like this:

`\frac{Cats}{\text{Dogs}}=(4)/(5)`

Now, we can solve for cats, like this:

`\begin{gathered} \text{Dogs}*\frac{Cats}{\text{Dogs}}=(4)/(5)\text{Dogs} \\ \text{Cats}*\frac{Dogs}{\text{Dogs}}=(4)/(5)\text{Dogs} \\ \text{Cats}*1=(4)/(5)\text{Dogs} \\ \text{Cats}=(4)/(5)\text{Dogs} \end{gathered}`

And we can express the total number of animals like this:

`\begin{gathered} Dogs+Cats=Animals=27 \\ \end{gathered}`

We can replace cats, and find the value of Dogs like this:

`\begin{gathered} \text{Dogs}+\text{Cats}=27 \\ \text{Dogs}+(4)/(5)\text{Dogs}=27 \\ \text{Dogs}(1+(4)/(5))=27 \\ \text{Dogs}(4+5)/(4)=27 \\ \text{Dogs}(9)/(5)=27 \\ \text{Dogs}(9)/(5)*(5)/(9)=27*(5)/(9) \\ \text{Dogs}=(27*5)/(9)=(135)/(9)=15 \end{gathered}`

And as the total amount of dogs is 15 and we use 5 small rectangles to represent them, we can find the value of each rectangle like this:

`\text{value of each regtangle=}(15)/(5)=3`