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

True

Step-by-step explanation:

In this question, we are expected to evaluate the validity of a particular proposition.

To evaluate this validity, what we do is that we check if the calculations as projected on the question are correct.

Let’s proceed!

Number of dogs to cat ratio = 4:5

Number of animals is 270;

Number of dogs will be 4/9 * 270 = 120

Number of cats will be 5/9 * 270 = 150

Now let’s check if the number of dogs is 4/5 that of cats.

Obviously 4/5 * 150 = 120

This makes true, the statement

The statement is true

Step-by-step explanation:

Total number of animals on the rescue farm = 270 animals

The given ratio of dogs in the farm is 4

The given ratio of cats in the farm is 5

To find the number of dogs on the farm,

= 4 / (4+5) × 270

= 4 /9 × 270

= 120

Therefore the number of dogs on the farm = 120.

To find the number of cats on the farm,

= 5/ (4+5) × 270

= 5/9 × 270

= 150

Therefore the number of cats on the farm = 150

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

Let's confirm the statement above.

Number of cats as calculated above = 150

Therefore,

The number of dogs = 4/5 × number of cats

The number of dogs = 4/5 × 150

The number of dogs = 120

Therefore, the statement :

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