Question

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?

Answer 1

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.

Explanation:

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

According to the question:

⇒
`c+d=270` ...equation (i)

Arranging the ratio:

⇒
`(4)/(5) = (d)/(c)`

⇒
`4c=5d`

⇒
`c=((5)/(4))d` ...equation (ii)

Plugging (ii) in equation (i).

⇒
`c+d=270`

⇒
`(5)/(4) d+d=270`

⇒
`(5d+4d)/(4) =270`

⇒
`9d=270* 4`

⇒
`d=(270* 4)/(9)`

⇒
`d=120`

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.

⇒
`(4)/(5) * 150`

⇒
`(4* 150)/(5)`

⇒
`120`

Statement is true.

b.

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

⇒
`(4)/(5) * 270`

⇒
`216`

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒
`c-d =30`

⇒
`150-120=30`

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.

⇒
`(5)/(9) * 270`

⇒
`150`

Statement is true.

So,

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