A dairy farmer wants to mix a 20% protein supplement and a standard 10% protein ration to make 1200 pounds of a high-grade 15% protein ration. How many pounds of each should he use?
Why did the dairy farmer bring his cows to the comedy club?
Because he heard they were in need of some fresh milkshakes! 🐄🥛
Now, let's calculate the pounds of each ingredient he needs to make that high-grade 15% protein ration. Let's call the pounds of the 20% protein supplement "x" and the pounds of the 10% protein ration "y".
To solve this, we'll set up a system of equations based on the protein percentages and the total weight:
Equation 1: x + y = 1200 (total weight is 1200 pounds)
Equation 2: (0.2x + 0.1y)/(x + y) = 0.15 (protein percentage should be 15%)
But remember, we like to keep things light, so let's round these numbers for simplicity:
Equation 2 (simplified): 2x + y = 1800
Now, let's solve this chucklesome problem:
Multiply Equation 1 by 2: 2x + 2y = 2400
Subtract Equation 2 from the above equation: (2x + 2y) - (2x + y) = 2400 - 1800
That simplifies to: y = 600
Plug the value of y into Equation 1: x + 600 = 1200
Solving for x: x = 600
So, the dairy farmer should use 600 pounds of the 20% protein supplement and 600 pounds of the 10% protein ration to make his 1200-pound high-grade 15% protein ration.
Just remember, no matter how you slice it or milk it, the cows will always be the "moo-sicians" in the dairy band! 🎵🎶
To solve this problem, let's denote the amount of the 20% protein supplement by x (in pounds) and the amount of the 10% protein ration by y (in pounds).
Step 1: Set up the system of equations based on the given information:
Equation 1: x + y = 1200 (to represent that the total weight is 1200 pounds)
Equation 2: 0.2x + 0.1y = 0.15 * 1200 (to represent the protein content)
Step 2: Solve the first equation for x:
x = 1200 - y
Step 3: Substitute the value of x into the second equation:
0.2 * (1200 - y) + 0.1y = 0.15 * 1200
Step 4: Simplify the equation:
240 - 0.2y + 0.1y = 180
Step 5: Combine like terms:
-0.1y = -60
Step 6: Divide both sides by -0.1:
y = 600
Step 7: Substitute the value of y into the first equation to find x:
x + 600 = 1200
x = 1200 - 600
x = 600
Therefore, the dairy farmer should use 600 pounds of the 20% protein supplement and 600 pounds of the 10% protein ration to make 1200 pounds of a high-grade 15% protein ration.
To solve this problem, we can use the concept of weighted averages. Let's break it down step by step:
Step 1: Assign variables:
Let's assign the following variables:
- x = pounds of the 20% protein supplement
- y = pounds of the 10% protein ration
Step 2: Set up equations:
We know that the total weight of the mixture is 1200 pounds, so we can write the equation:
x + y = 1200
We also know that the protein percentage of the mixture should be 15%, so we can write the equation:
0.20x + 0.10y = 0.15 * 1200
Step 3: Solve the equations:
Now, we have a system of two equations. We can use substitution or elimination to solve them.
Using the first equation, we can rewrite it as:
x = 1200 - y
Substitute this value of x into the second equation:
0.20(1200 - y) + 0.10y = 0.15 * 1200
Simplify the equation:
240 - 0.20y + 0.10y = 180
Combine like terms:
0.10y = 180 - 240
0.10y = -60
Divide by 0.10 to solve for y:
y = -60 / 0.10
y = 600
Step 4: Calculate the remaining variable:
Now that we know y = 600 pounds, we can substitute it back into the first equation to find x:
x = 1200 - y
x = 1200 - 600
x = 600
So, the dairy farmer should use 600 pounds of the 20% protein supplement and 600 pounds of the 10% protein ration to make 1200 pounds of a high-grade 15% protein ration.
If there are x lbs of the 20% protein, then the rest (1200-x) is 10%.
So, adding up the amounts of protein, it must equal the total:
.20x + .10(1200-x) = .15(1200)
Since 15% is halfway between 10% and 20%, expect the mix to be half and half.