The ratio of the number of dogs the number of cats is 4:5. There are 270 animals on the rescue Farm. The number of dogs is 4/5. True or false?

Here is the complete question:

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒   ...equation (i)

Arranging the ratio:

⇒

⇒

⇒    ...equation (ii)

Plugging (ii) in equation (i).

⇒

⇒

⇒

⇒

⇒

⇒

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

a.

The number of dogs is 4/5 the number of cats.

⇒

⇒

⇒

Statement is true.

b.

4/5 of the pets at the farm are dogs.

⇒

⇒

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒

⇒

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

5/9 of the pets at the farm are cats.

⇒

⇒

Statement is true.

So,

Statement  a,c and e are true as we could observe in the explanation.

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