Respuesta :
Answer:
81 sheep were there on the farm
Step-by-step explanation:
Consider the provided information.
Let x represents the number of goats.
y represents the number of cows.
z represents the number of sheep.
Therefore, the total number of animals are x+y+z
2/5 of the animals were goats. This can be written as:
[tex]\frac{2}{5}(x+y+z)=x[/tex]
There were three times as many sheep than cows.
[tex]z=3y[/tex]
There were 45 more goats than cows,
[tex]x=45+y[/tex]
Substitute the value of x and z in equation 1.
[tex]\frac{2}{5}(45+y+y+3y)=45+y[/tex]
[tex]\frac{2}{5}(45+5y)=45+y[/tex]
[tex]2(9+y)=45+y[/tex]
[tex]18+2y=45+y[/tex]
[tex]y=27[/tex]
Hence, there are 27 cows.
Substitute the value of y in [tex]x=45+y[/tex]
[tex]x=45+27[/tex]
[tex]x=72[/tex]
Therefore, there are 72 goats.
Substitute the value of y in [tex]z=3y[/tex]
[tex]z=3(27)[/tex]
[tex]z=81[/tex]
Thus, there are 81 sheep.
