Question

Someone please help I’m completely lost

Answer 1

There are 84 cattle, 70 sheep and 35 pigs

Explanation:

We're told three things:

1. For every six cows, there are five sheep
2. For every two sheep, there is one pig
3. There are 189 animals in total

Starting off, let's express the the last point as an equation:

c + s + p = 189

To solve this, we need to eliminate variables by substituting others in their place. Let's start with cattle to sheep. Using the 6:5 ratio of cattle to sheep:

c / 6 = s / 5

s = 5c / 6

Let's update our equation to match that

c + 5c / 6 + p = 189

Now to eliminate pigs. We know that there is one pig for every two sheep. So:

p = s / 2

We can substitute our relationship with cattle to sheep in to that to express p as a function of c:

p = (5c / 6) / 2

p = 5c / 12

Now we can substitute that into the original equation

c + 5c / 6 + 5c / 12 = 189

Now we can solve for c:

c + 5c / 6 + 5c / 12 = 189

12c / 12 + 10c / 12 + 5c / 12 = 189

(12 + 10 + 5)c / 12 = 189

27c / 12 = 189

9c / 4 = 189

9c = 756

c = 84

So there are 84 cattle. We can use the original given relationships to find the rest.

s = 5 × 84 / 6

s = 5 × 14

s = 70

p = s / 2

p = 70 / 2

p = 35

So there are 84 cattle, 70 sheep and 35 pigs

Let's double check:

84 + 70 + 35 = 189 - correct

70 / 2 = 35 - correct

5 * 84 / 6 = 70 - correct

So the answer is correct.

Answer 2

70

Explanation:

cows:sheep=6:5

sheep:pigs=2:1

cows:sheep:pigs=12:10:5

27x=189

x=7

sheep=10*7

sheep=70