soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360-lb mixture the is 15% protein.
.18s+.09c
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360 =.15
18s+9c=5400
s+c=360
now I am lost. appreciate any help
To solve this problem, you can set up a system of equations based on the given information.
Let's define s as the number of pounds of soybean meal, and c as the number of pounds of cornmeal.
From the first piece of information, we know that the protein content of soybean meal is 18%, which means that 0.18s pounds of protein come from soybean meal.
Similarly, the protein content of cornmeal is 9%, so 0.09c pounds of protein come from cornmeal.
We want to create a mixture that has a total weight of 360 pounds (s + c = 360) and a protein content of 15% (0.15 * 360 = 0.18s + 0.09c).
Now we have two equations:
Equation 1: s + c = 360 (from the total weight of the mixture)
Equation 2: 0.18s + 0.09c = 0.15 * 360 (from the protein content)
To solve the system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
1. Solve equation 1 for one variable in terms of the other. Let's solve for s:
s = 360 - c
2. Substitute the value of s into equation 2:
0.18(360 - c) + 0.09c = 54
3. Expand and simplify:
64.8 - 0.18c + 0.09c = 54
4. Combine like terms:
-0.09c = 54 - 64.8
-0.09c = -10.8
5. Divide both sides by -0.09:
c = -10.8 / -0.09
c = 120
6. Substitute the value of c into equation 1 to solve for s:
s = 360 - c
s = 360 - 120
s = 240
Therefore, you should mix 240 pounds of soybean meal with 120 pounds of cornmeal to get a 360-pound mixture that is 15% protein.
Method 2: Elimination
1. Multiply equation 1 by -0.18 to make the coefficients of s in equations 1 and 2 cancel out:
-0.18s - 0.18c = -0.18 * 360
2. Write out equation 2 as is:
0.18s + 0.09c = 54
3. Add the modified equation 1 and equation 2 together:
-0.18s - 0.18c + 0.18s + 0.09c = -64.8 + 54
4. Simplify and combine like terms:
-0.09c = -10.8
5. Divide both sides by -0.09:
c = -10.8 / -0.09
c = 120
6. Substitute the value of c into equation 1 to solve for s:
s = 360 - c
s = 360 - 120
s = 240
Again, you find that you should mix 240 pounds of soybean meal with 120 pounds of cornmeal to get a 360-pound mixture that is 15% protein.