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

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:

$\frac{2}{5}(x+y+z)=x$

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.

$\frac{2}{5}(45+y+y+3y)=45+y$

$\frac{2}{5}(45+5y)=45+y$

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

$18+2y=45+y$

$y=27$

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.