Rancher had equal number of sheep and cows. When the rancher was asleep wolves slaughtered?

Question

The rancher had equal number of sheep and cows. When the rancher was asleep wolves slaughtered 1/3 of all sheep, and 1/6 of all cows.

The rancher counted that 60 animals were slaughtered.
How many sheep and cows has the rancher now?

Answer 1

Since the number of sheep and cows are equal, the number of sheep lost would be 1/6 of the total animals. And the number of cows lost would be 1/12 of the total animals. All together this is:
1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4

If 60 animals is 1/4 of the total, he started with 240 animals (120 of each).

1/3 of the sheep (40) were killed leaving 80 sheep
1/6 of the cows (20) were killed leaving 100 sheep

Answer 2

s = # of sheep
c = # of cows

equal number of sheep and cows

1) s = c

When the rancher was asleep wolves slaughtered 1/3 of all sheep, and 1/6 of all cows. The rancher counted that 60 animals were slaughtered.

2) s/3 + c/6 = 60

c/3 + c/6 = 60

2c/6 + c/6 = 60

3c/6 = 60

3c = 360

c = 120

He had before 120 sheep, 120 cows

(1/3)120 = 40 -> 80 sheep left

(1/6)120 = 20 -> 100 cows left

Answer 3

He has 100 cows and 80 sheep.

Since the number of sheep and cows were equal, we can say that half of his animals were sheep, and half were cows.

That means that the dead sheep were 1/6 (or 2/12) of his stock, and the dead cows were 1/12. Which also means that he lost 3/12 or 1/4 of his animals. If 60 animals = 1/4, then his original count was 240, or 120 sheep and 120 cows.

1/3 of 120 = 40, and 1/6 = 20.
120-40 = 80 sheep.
120-20 = 100 cows.

Answer 4

since the number of sheep and cows are the same:
x=#sheep
x=#cows
1/3x +1/6x = 60
2x/6 + 1/6x = 60
3x/6 = 60
therefore x =120
to get total number of animals before slaughter (y)
x + x = y
120 + 120 = 240
240 - 60 = 180
180 is the total amount of animals the rancher has now.

Answer 5

s = total number of sheep
c = total number of cow

The rancher had equal number of sheep and cows.
s = c

the wolf slaughtered of all sheep. so s/3 is the number of sheep which got slaughtered

the wolf slaughtered 1/6 of all cows. c/6 is the numbe of cows which got slaughtered

60 animials got slaughtered, including both sheep and cows
s/3 + c/6 = 60

substitute
c/3 + c/6 = 60
c/2 = 60
c = 120

s = total number of sheep
c = total number of cow

The rancher had equal number of sheep and cows.
s = c

the wolf slaughtered of all sheep. so s/3 is the number of sheep which got slaughtered

the wolf slaughtered 1/6 of all cows. c/6 is the numbe of cows which got slaughtered

60 animials got slaughtered, including both sheep and cows
s/3 + c/6 = 60

substitute
c/3 + c/6 = 60
c/2 = 60
c = 120

before the animails got slaughtered, the rancher has 120 sheep and 120 cows

1/3 of the sheep are gone. 120 - (1/3)(120) = 80 sheep are left

1/6 of the cows ar gone. 120 - (1/6)(120) = 100 cows are left

so he now has 80 sheep and 100 cows

Answer 6

80 Sheep
100 Cows