8 bags of cattle feed are needed to feed 4 cows for 2 months. How long will the same feed last to feed 6 cows?

The correct answer is: Hence, the small feed will last for 1 1/3 to feed 6 cows.

Let the number of bags of cattle be represented as x, the number of cows be represented as y and the number of months be represented as z. Now, more cows will mean more bags of cattle are required so x and y will have a directly proportional relationship i.e
y  x
Now if there are more cows this means the bags of cattle will last for fewer months which means x and z have an inversely proportional relationship i.e
y  
So, we can say that
y  
y =  …….(1)
Where k is a proportionality constant
Step 1 of 2:
It is given that 8 bags of cattle feed are needed to feed 4 cows for 2 months. So, x = 8, y = 4 and z = 2. Putting the values in equation (1)
4 = 
k =  = 1
Step 2 of 2:
Now we are asked to find the number of months the same feed will last to feed 6 cows. So, x = 8, y = 6 and we need to find z. Putting the values in equation (1)
6 = 
Now, put the value of k = 1
z = 
d =  =  months
Final Answer:
Hence, the small feed will last for  to feed 6 cows.