soybean meal is 12% protein and corn meal is 6% protein how many pounds of each should be mixed together in order to get 240 pounds mixer that is 8% protein?
help pleae??
let the amount of soybean meal be x
then the amount of cornmeal is 240-x
so .12x + .06(240-x) = .08(240)
I would now multiply each term by 100
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Im not good at algebra what do i multiply?
.12x + .06(240-x) = .08(240)
Both sides multiplied by 100.
12x + 6(240-x) = 8(240)
Get rid of the parentheses by multiplying again.
I hope this helps a little more.
To solve this problem, we can set up a system of equations.
Let's denote the pounds of soybean meal as "x" and the pounds of corn meal as "y". We are given the following information:
- Soybean meal is 12% protein, so the amount of protein in soybean meal is 0.12 * x.
- Corn meal is 6% protein, so the amount of protein in corn meal is 0.06 * y.
- The total weight of the mixture is 240 pounds, so x + y = 240.
- The mixture is 8% protein, so the amount of protein in the mixture is 0.08 * (x + y).
We can now set up the equations:
0.12 * x + 0.06 * y = 0.08 * 240
x + y = 240
Now, we can solve this system of equations.
First, let's simplify the first equation by multiplying both sides by 100 to get rid of the decimals:
12x + 6y = 8 * 240
x + y = 240
Now, we can solve the system of equations using substitution or elimination. Let's use elimination:
Multiply the second equation by 12 to match the coefficient of x in the first equation:
12x + 12y = 12 * 240
x + y = 240
Now, subtract the second equation from the first equation:
12x + 6y - (x + y) = 12 * 240 - 240
11x + 5y = 2760
Simplify:
11x + 5y = 2760
Now, we have one equation with one variable. We can solve for x:
x = (2760 - 5y) / 11
We need to find values of x and y that will satisfy all the conditions. Since we want to mix a total of 240 pounds and x represents the pounds of soybean meal, we know that x must be less than or equal to 240.
To determine the value of y, we can substitute the value of x into the second equation:
x + y = 240
(2760 - 5y) / 11 + y = 240
Solve for y:
(2760 - 5y + 11y) / 11 = 240
2760 + 6y = 11 * 240
2760 + 6y = 2640
6y = 2640 - 2760
6y = -120
y = -120 / 6
y = -20
Since we cannot have a negative weight of corn meal, this solution is not feasible.
In conclusion, it is not possible to mix 240 pounds of a mixture with 8% protein using soybean meal (12% protein) and corn meal (6% protein).