A farmer finds that he can buy 5 sheep and 5 cows for $129 or 10 sheep and 17 cows for $177.how much will it cost him to buy 3 sheeps and 2 cows?
Let s represent the sheep, and c represent the cows
5s + 5c = 129
10s + 17c = 177
Your choice is to use elimination or substitution to solve for c and s.
If you multiply 5s + 5c = 129 by -2 and then add it to the second equation it works out nicely and you can solve for c
-10s - 10c = -645
10s + 17c = 177
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7c = -645 + 177 and solve for c, then sub it back in to solve for s...
the answer is not correct b/c
5s + 5c = 129 when multiply by -2 it became
-10s - 10c = -258; not -10s - 10c = -645
finally c= -81/7
To find out how much it will cost to buy 3 sheep and 2 cows, we first need to determine the cost of 1 sheep and 1 cow.
Let's assign variables to represent the cost of a sheep and a cow. We'll call the cost of a sheep "S" and the cost of a cow "C."
According to the information given, the farmer can buy 5 sheep and 5 cows for $129. This can be represented by the equation:
5S + 5C = 129
Similarly, the farmer can buy 10 sheep and 17 cows for $177. This can be represented by the equation:
10S + 17C = 177
We have a system of two equations with two variables. We can solve this system of equations to find the values of S and C.
Multiplying the first equation by 2, we get:
10S + 10C = 258
Now, we subtract the second equation from the modified first equation to eliminate the S term:
(10S + 10C) - (10S + 17C) = 258 - 177
10S + 10C - 10S - 17C = 81
-7C = 81
C = 81 / -7
C ≈ -11.5714
With the value of C, we can substitute it back into one of the original equations to solve for S. Let's use the first equation:
5S + 5C = 129
5S + 5(-11.5714) = 129
5S - 57.857 = 129
5S = 129 + 57.857
5S ≈ 186.857
S ≈ 186.857 / 5
S ≈ 37.3714
So, the cost of one sheep (S) is approximately $37.37, and the cost of one cow (C) is approximately $-11.57 (meaning the farmer receives money for buying each cow).
Now that we know the cost of one sheep and one cow, we can calculate the total cost of 3 sheep and 2 cows:
3S + 2C = (3 * 37.37) + (2 * -11.57)
= 112.11 - 23.14
≈ $88.97
Therefore, it will cost the farmer approximately $88.97 to buy 3 sheep and 2 cows.