Soybean meal is 18% protein, cornmeal is 9% protein. how many pounds of each should be mixed together to get a 360 pound mixture that is 15% protein ?
Word problems are my favorites, but this one is confusing me. Help is very much appreciated
.18 s + .09 p = .15(s+p)
and
s+p=360
If I did this correctly it is 120 lbs cornmeal, 240 lbs soy
To solve this problem, you can set up a system of equations based on the given information.
Let's assume we need x pounds of soybean meal and y pounds of cornmeal.
From the problem, we know:
1) The total weight of the mixture is 360 pounds:
x + y = 360
2) The protein content in the soybean meal is 18%:
0.18x
3) The protein content in the cornmeal is 9%:
0.09y
4) The total protein content in the mixture should be 15%:
0.15(360)
Now, we can set up the equation based on the protein content in the mixture:
0.18x + 0.09y = 0.15(360)
To solve this system of equations, first, multiply 0.15 by 360:
0.18x + 0.09y = 54
Now, you can solve the system of equations using different methods such as substitution or elimination.
One straightforward method is to multiply both sides of the first equation (x + y = 360) by 0.09 to match the coefficients of y:
0.09x + 0.09y = 32.4
Next, subtract this equation from the equation we obtained earlier (0.18x + 0.09y = 54):
0.18x + 0.09y - (0.09x + 0.09y) = 54 - 32.4
0.18x - 0.09x = 21.6
0.09x = 21.6
x = 240
Now, substitute the value of x back into the first equation:
240 + y = 360
y = 120
Therefore, to get a 360-pound mixture with 15% protein, you would need 240 pounds of soybean meal and 120 pounds of cornmeal.