A famer has twice as many cow as sheep. After he sold 375 cows and another 12 cows died, he had half as many cows as sheep left. How many cows remained.
C=2S
Now, with C-375-12, then
2(C-375-12)=S
PUt the first equation into the second..
2(C-375-12)=C/2
1.5C=2*(387)
C=4/3*387= 4*129=516 and S=258
Now in the end, number of cows=
516-375-12= 129 and S=258
To solve this problem, let's break it down step by step.
Let's assume the number of sheep the farmer has is S and the number of cows is C.
From the information given, we can form two equations:
1) C = 2S (The farmer has twice as many cows as sheep)
2) (C - 375 - 12) = 1/2(S) (After selling 375 cows and 12 dying, he had half as many cows as sheep left)
Let's substitute the value of C from equation 1 into equation 2:
(2S - 375 - 12) = 1/2(S)
Now we can solve for S:
2S - 375 - 12 = 1/2S
Multiplying both sides by 2 to get rid of the fraction:
4S - 750 - 24 = S
Combining like terms:
3S - 774 = 0
Adding 774 to both sides:
3S = 774
Dividing both sides by 3:
S = 774 / 3
Simplifying:
S = 258
Now we know the number of sheep the farmer has is 258. Let's substitute this value back into equation 1 to find the number of cows:
C = 2S
C = 2(258)
C = 516
Therefore, the number of cows remaining after selling 375 cows and 12 cows dying is 516 - 375 - 12 = 129.