I have a problem that I need help with can someone show me the steps
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Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each shoul be mixed to get a 350-lb mixture that is 12% protein?
Why do i never get any help
let the amount of 16% mix to be added be x lb
let the amount of 9% mix to be added be 350-x lb
.16x + .09(350-x) = .12(350)
multiply by 100
16x + 9(350-x) = 12(350)
16x + 3150 - 9x = 4200
7x = 1050
x = 150
then 350-x = 200
They should use 150 lb of the 16% mix and
200 lb of the 9% mix
Thank you
To solve this problem, you can set up a system of equations based on the given information. Let's call the number of pounds of soybean meal "x" and the number of pounds of cornmeal "y."
1. The first equation represents the total weight of the mixture:
x + y = 350
2. The second equation represents the protein content of the mixture:
(0.16x + 0.09y) / 350 = 0.12
To get the protein content, you divide the total protein in the mixture (0.16x + 0.09y) by the total weight of the mixture (350 pounds) and set it equal to the desired protein content (0.12 or 12%).
Now, you have a system of equations:
x + y = 350
(0.16x + 0.09y) / 350 = 0.12
To solve this system of equations, you can use the method of substitution or elimination.
Let's solve it using the method of substitution:
1. Rearrange the first equation to express "x" in terms of "y":
x = 350 - y
2. Substitute the expression for "x" into the second equation:
(0.16(350 - y) + 0.09y)/350 = 0.12
3. Simplify and solve for "y":
(56 - 0.16y + 0.09y)/350 = 0.12
(56 - 0.07y)/350 = 0.12
56 - 0.07y = 0.12 * 350
56 - 0.07y = 42
4. Solve for "y":
-0.07y = 42 - 56
-0.07y = -14
y = -14 / -0.07
y = 200
Now that you have the value of "y", substitute it back into the first equation to find the value of "x":
x + 200 = 350
x = 350 - 200
x = 150
Therefore, to create a 350-lb mixture with a 12% protein content, you should mix 150 pounds of soybean meal and 200 pounds of cornmeal.