soybean meal is 12% protein; cornmeal is 6% protein.How many pounds of each should be mixed together in order to get 240-lb mixture that is 10% protein%
How many pounds of the cornmeal should be in the mixture?_____pounds
How many pounds of the soybeans meals should be in the mixture?______pounds
Try this.
Let S = pounds of soy bean meal.
Let C = pounds of corn meal.
so one equation is
S + C = 240
The other equation is
0.12S + 0.06S = 0.1*240
Solve the two equations for the two unknowns.
To solve this problem, we can set up a system of equations based on the given information:
Let's assume x represents the number of pounds of cornmeal and y represents the number of pounds of soybean meal.
1. The total weight of the mixture is 240 pounds:
x + y = 240 ----(Equation 1)
2. The protein content in the cornmeal is 6%, and the protein content in the soybean meal is 12%. The total weight of the mixture is 240 pounds, and the protein content should be 10%:
(0.06x + 0.12y) / 240 = 0.10 ----(Equation 2)
To solve this system of equations, we can use the method of substitution:
1. Solve Equation 1 for x:
x = 240 - y
2. Substitute the value of x in Equation 2:
(0.06(240 - y) + 0.12y) / 240 = 0.10
3. Simplify and solve for y:
14.4 - 0.06y + 0.12y = 24
0.06y = 24 - 14.4
0.06y = 9.6
y = 9.6 / 0.06
y = 160
Therefore, there should be 160 pounds of soybean meal in the mixture.
4. Substitute the value of y back into Equation 1 to find x:
x + 160 = 240
x = 240 - 160
x = 80
Therefore, there should be 80 pounds of cornmeal in the mixture.
To summarize:
The number of pounds of cornmeal in the mixture is 80 pounds.
The number of pounds of soybean meal in the mixture is 160 pounds.
To solve this problem, we can use a system of equations. Let's assign variables to the unknown quantities:
Let x be the number of pounds of soybean meal and y be the number of pounds of cornmeal in the mixture.
The total weight of the mixture is given as 240 pounds, so we have the equation: x + y = 240.
The protein content in the soybean meal is 12% and the protein content in the cornmeal is 6%. We want to create a mixture that is 10% protein, so we have the equation: (0.12x + 0.06y) / 240 = 0.10.
Let's solve this system of equations:
1. Simplify the second equation by multiplying both sides by 240 to remove the denominator: 0.12x + 0.06y = 0.10 * 240.
Simplifies to: 0.12x + 0.06y = 24.
2. Next, we can use the first equation to solve for x: x = 240 - y.
3. Substitute this value for x in the simplified second equation: 0.12(240 - y) + 0.06y = 24.
Simplify further: 28.8 - 0.12y + 0.06y = 24.
Combine like terms: 28.8 - 0.06y = 24.
Subtract 28.8 from both sides: -0.06y = -4.8.
Divide both sides by -0.06: y = 80.
4. Now we can substitute the value of y back into the first equation to find x: x + 80 = 240.
Subtract 80 from both sides: x = 160.
So, the number of pounds of cornmeal in the mixture is 80 pounds, and the number of pounds of soybean meal in the mixture is 160 pounds.
so the answer would be
s=44lbs
c=4.09lbs