A farmer has two blends of grain, one 50% barley and the other 20% barley. How many pounds of each
each blend should be used to create a 45 pound mix that is 30% barley ?
.50x + .20(45-x) = .30(45)
nope
To solve this problem, we can use a system of linear equations. Let's assign variables to the two blends of grain:
Let's call the amount of the 50% barley blend "x" (in pounds) and the amount of the 20% barley blend "y" (in pounds).
Now let's set up the equations based on the given information:
Equation 1: Total weight equation
The total weight of the mixture should be 45 pounds:
x + y = 45
Equation 2: Barley percentage equation
The barley percentage in the mixture should be 30%:
(0.5x + 0.2y)/(x + y) = 0.3
Now we have a system of two equations. We can solve this system by substitution or elimination.
Let's solve it by substitution:
From Equation 1, we can express x in terms of y:
x = 45 - y
Now substitute this expression for x in Equation 2:
(0.5(45 - y) + 0.2y)/(45) = 0.3
Simplifying this equation, we get:
(22.5 - 0.5y + 0.2y) / 45 = 0.3
22.5 - 0.3y = 0.3(45)
22.5 - 0.3y = 13.5
-0.3y = 13.5 - 22.5
-0.3y = -9
y = -9 / -0.3
y = 30
Now substitute the value of y back into Equation 1 to find x:
x + y = 45
x + 30 = 45
x = 45 - 30
x = 15
Therefore, the farmer should use 15 pounds of the 50% barley blend and 30 pounds of the 20% barley blend to create a 45-pound mix that is 30% barley.