Question

There are some goats, cows and, sheep. 2/5 of the animals were goats. There were three times as many sheep than cows. If there were 45 more goats than cows, how n=many sheep were there on the farm

Answer 1

81 sheep were there on the farm

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:

`(2)/(5)(x+y+z)=x`

There were three times as many sheep than cows.

`z=3y`

There were 45 more goats than cows,

`x=45+y`

Substitute the value of x and z in equation 1.

`(2)/(5)(45+y+y+3y)=45+y`

`(2)/(5)(45+5y)=45+y`

`2(9+y)=45+y`

`18+2y=45+y`

`y=27`

Hence, there are 27 cows.

Substitute the value of y in
`x=45+y`

`x=45+27`

`x=72`

Therefore, there are 72 goats.

Substitute the value of y in
`z=3y`

`z=3(27)`

`z=81`

Thus, there are 81 sheep.