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
please, please answer

Answer 1

see the procedure

Explanation:

Let

x ----> the number of dogs

y ---> the number of cats

we know that

The ratio of the number of dogs to the number of cats is 4:5

so

`(x)/(y)=(4)/(5)`

`x=(4)/(5)y` ----> equation A

That means ---> The number of dogs is 4/5 the number of cats

There are 270 animals on the rescue farm

so

`x+y=270` ----> equation B

Substitute equation A in equation B

`(4)/(5)y+y=270`

solve for y

`(9)/(5)y=270`

`y=270(5)/9\\y=150\ cats`

Find the value of x

`x=(4)/(5)(150)=120\ dogs`

Verify each statement

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

The statement is true (see the explanation)

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

The statement is false

Because

(4/5)(270)=216 dogs

The number of dogs is 120 not 216 (see the explanation)

c) There are exactly 30 more cats than dogs

The statement is true

Because, there are 150 cats and 120 dogs (see the explanation)

d) There are exactly 30 dogs at the farm

The statement is false

Because, there are 120 dogs in the farm (see the explanation)

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

The statement is true

Because

(5/9)270=150 cats

The number of cats is 150 (see the explanation)