farmer joe needs cows pigs an chickens
cows cost 10.00 each and pigs cost .50 cents each,an chickens are 10 cents.he needs 100 animals an he only has 100 dollars .
let x=cow, y=pig, and z=chicken
10x + .5y +.1z = 100
x + y + z = 100
substitute & get the answer.
To solve the system of equations given, you can use substitution. Here's how you can proceed:
1. Start with the given equations:
10x + 0.5y + 0.1z = 100 (Equation 1)
x + y + z = 100 (Equation 2)
2. Solve Equation 2 for one of the variables. Let's solve it for x:
x = 100 - y - z (Equation 3)
3. Substitute Equation 3 into Equation 1:
10(100 - y - z) + 0.5y + 0.1z = 100
4. Simplify and rearrange the equation:
1000 - 10y - 10z + 0.5y + 0.1z = 100
-9.5y - 9.9z = 0
5. Divide both sides of the equation by -9.9 to isolate one of the variables. Let's solve for y:
y = -0.1z (Equation 4)
6. Now, substitute Equation 4 into Equation 3 to solve for x:
x = 100 - (-0.1z) - z
x = 100 + 0.1z - z
x = 100 - 0.9z (Equation 5)
7. Substitute Equations 4 and 5 into Equation 2:
100 - 0.9z + (-0.1z) + z = 100
8. Simplify and solve for z:
1z = 0
9. Since z = 0, substitute this value back into Equation 5 to find x:
x = 100 - 0.9(0)
x = 100
10. Substitute the values of x and z into Equation 4 to find y:
y = -0.1(0)
y = 0
11. Therefore, the solution to the system of equations is:
x = 100, y = 0, z = 0
In this case, it means that Farmer Joe can buy 100 cows, 0 pigs, and 0 chickens with his $100 budget.