There are 84 cattle, 70 sheep and 35 pigs
Step-by-step explanation:
We're told three things:
For every six cows, there are five sheepFor every two sheep, there is one pigThere 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.