Question

The constant of proportionality in terms of dogs per kennel is 3, and there are 27 dogs in the shelter. How many kennels are there?

Answer 1

Answer:

Answer: The correct option is (A) 9.

Step-by-step explanation: Given that in a shelter, the number of kennels is proportional to the number of dogs. The constant of proportionality in terms of dogs per kennel is 3, and there are 27 dogs in the shelter.

We are to find the number of kennels.

Let k and d represents the number of kennels and dogs respectively in the shelter.

Then, according to the given information, we have

\begin{gathered}k\propto d\\\\\Rightarrow d\propto k\\\\\Rightarrow d=tk~~~~~~~\textup{[where t is the proportionality constant]}\\\\\Rightarrow \dfrac{d}{k}=t.\end{gathered}

k∝d

⇒d∝k

⇒d=tk [where t is the proportionality constant]

⇒

k

d

=t.

Since constant of proportionality in terms of dogs per kennel is 3, so we have

t = 3. That is,

\begin{gathered}\dfrac{d}{k}=3\\\\\\\Rightarrow k=\dfrac{d}{3}\end{gathered}

k

d

=3

⇒k=

3

d

When d = 27, then

k=\dfrac{27}{3}=9.k=

3

27

=9.

Thus, the number f kennels is 9.

Option (A) is CORRECT.