Answer:
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 sheep
- For every two sheep, there is one pig
- 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.
