Ground beef sells for $4.75 per kg and ground pork sells for $5.50 per kg. How many kg of ground pork should be mixed with 8 kg of ground beef to make a mixture that sells for $5.10 per kg?
I don't know how to set this up or anything. Please help!
To solve this problem, you need to set up an equation based on the information given.
Let's assume that x represents the amount of ground pork (in kg) that needs to be mixed with 8 kg of ground beef.
Now, let's set up the equation based on the prices and amounts of the meats:
(Price of ground beef × Amount of ground beef) + (Price of ground pork × Amount of ground pork) = Price of mixture × Total amount of mixture
Using the given information:
(4.75 × 8) + (5.50 × x) = 5.10 × (8 + x)
Let's simplify the equation:
38 + 5.50x = 40.8 + 5.10x
Now, let's solve for x:
5.50x - 5.10x = 40.8 - 38
0.4x = 2.8
Dividing both sides by 0.4:
x = 2.8 / 0.4
x = 7
Therefore, you should mix 7 kg of ground pork with 8 kg of ground beef to obtain a mixture that sells for $5.10 per kg.
To solve this problem, you can use a weighted average formula. Here's how you can set it up and solve it step by step:
Step 1: Determine the unknown variable
Let's assume the unknown variable is the amount of ground pork to be mixed with 8 kg of ground beef. Let's call it x (in kg).
Step 2: Establish the given information
- Ground beef sells for $4.75 per kg.
- Ground pork sells for $5.50 per kg.
- The mixture should sell for $5.10 per kg.
- The amount of ground beef is 8 kg.
Step 3: Set up the weighted average equation
The weighted average equation is given by:
(Price of Item A x Amount of Item A) + (Price of Item B x Amount of Item B) = Total Cost
In this case, Item A represents the ground beef, Item B represents the ground pork, and the total cost represents the final mixture.
So, the equation becomes:
(4.75 * 8) + (5.50 * x) = 5.10 * (8 + x)
Step 4: Simplify and solve the equation
First, distribute the 5.10 to the terms inside parentheses:
38 + (5.50 * x) = 40.80 + 5.10 * x
Next, simplify the equation by combining like terms:
5.50 * x - 5.10 * x = 40.80 - 38
0.40 * x = 2.80
Finally, solve for x by dividing both sides of the equation by 0.40:
x = 2.80 / 0.40
x ≈ 7
Therefore, you would need to mix approximately 7 kg of ground pork with 8 kg of ground beef to make a mixture that sells for $5.10 per kg.
Let x=weight of ground pork in kg
then 8-x=weight of ground beef.
total weight = 8 kg
therefore
5.50x + 4.75(8-x) = 5.10 * 8
Solve for x.