Respuesta :
Answer:
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:
⇒ [tex]c+d=270[/tex] ...equation (i)
Arranging the ratio:
⇒ [tex]\frac{4}{5} = \frac{d}{c}[/tex]
⇒ [tex]4c=5d[/tex]
⇒ [tex]c=(\frac{5}{4})d[/tex] ...equation (ii)
Plugging (ii) in equation (i).
⇒ [tex]c+d=270[/tex]
⇒ [tex]\frac{5}{4} d+d=270[/tex]
⇒ [tex]\frac{5d+4d}{4} =270[/tex]
⇒ [tex]9d=270\times 4[/tex]
⇒ [tex]d=\frac{270\times 4}{9}[/tex]
⇒ [tex]d=120[/tex]
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.
⇒ [tex]\frac{4}{5} \times 150[/tex]
⇒ [tex]\frac{4\times 150}{5}[/tex]
⇒ [tex]120[/tex]
Statement is true.
b.
4/5 of the pets at the farm are dogs.
⇒ [tex]\frac{4}{5} \times 270[/tex]
⇒ [tex]216[/tex]
Number of dogs = 120
So the above statement is false.
c.
There are exactly 30 more cats than dogs.
⇒ [tex]c-d =30[/tex]
⇒ [tex]150-120=30[/tex]
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.
⇒ [tex]\frac{5}{9} \times 270[/tex]
⇒ [tex]150[/tex]
Statement is true.
So,
Statement a,c and e are true as we could observe in the explanation.
