A farmer has enough food to last his 40 cattle 35 days. If he buys 50 cattle, how long can the same feed can last? Let X be the number of days the same feed can last
With 90 cattle, he has 9/4 as many mouths, so 4/9 as long to eat: about 16 days
To find the number of days the same feed can last for 50 cattle, we'll set up a proportion using the given information.
Let's assume that the amount of feed required for one cattle per day is F.
According to the problem, the farmer has enough food to last his 40 cattle 35 days. This means that the total food supply available is 40 cattle × 35 days = 1400 cattle-days.
Since we assumed that each cattle needs F amount of feed per day, the total amount of feed required for 40 cattle for 35 days is 40 × 35 × F.
Now, we want to find the number of days (X) the same feed can last for 50 cattle. We can set up the following proportion:
40 × 35 × F = 50 × X × F
Let's solve for X:
40 × 35 × F = 50 × X × F
(40 × 35) / (50 × F) = X
Now, we have the value of X, which represents the number of days the same feed can last for 50 cattle. We can simplify the expression:
40 × 35 = 50 × X
1400 = 50 × X
1400 / 50 = X
28 = X
Therefore, the same feed can last for 28 days for 50 cattle.