A grocer wants to mix nuts costing $5 per kg with nuts costing $8 per kg to make a 10 kg mixture selling for $6 per kg. How much of each type should be mixed?
How do I set up this problem? Thank you.
let E be weight of expensive nuts, C be cheaper nuts
E*8+C*5=10*6 value equation
E+C=10 mass equation
Solve it by any method, I will do determinants
Det: 8-5=3
E= (60-50)/3=10/3 =3.33 lb
C= 80-60 /3=20/3 =6.66 lb
To solve this problem, we can use the method of weighted averages.
Let's assume we need to mix x kg of nuts costing $5 per kg and y kg of nuts costing $8 per kg to obtain a total mixture of 10 kg.
Now, let's set up the equation based on the total cost of the mixture and its price per kg.
The total cost of the mixture is equal to the price per kg multiplied by the total weight of the mixture, which is 10 kg. So, the equation is:
(5x + 8y) = 6 * 10.
Additionally, we need to consider the total weight of the mixture, which is 10 kg. So, the equation is:
x + y = 10.
Now we have a system of equations:
5x + 8y = 60,
x + y = 10.
Solving this system will give us the values for x and y, representing the amount of each type of nuts needed to be mixed.
To set up this problem, we need to determine how much of each type of nut should be mixed to achieve the desired average price per kilogram.
Let's call the amount of nuts costing $5 per kg as x kg, and the amount of nuts costing $8 per kg as y kg.
Step 1: Write down the given information:
- Cost of nuts costing $5 per kg = $5
- Cost of nuts costing $8 per kg = $8
- Total weight of the mixture = 10 kg
- Average price of the mixture = $6 per kg
Step 2: Set up the equation for the total cost of the nuts mixture:
Total Cost = Cost of nuts costing $5 per kg + Cost of nuts costing $8 per kg
The cost of nuts weighing x kg at $5 per kg is 5x dollars.
The cost of nuts weighing y kg at $8 per kg is 8y dollars.
So, the equation becomes:
5x + 8y = Total Cost
Step 3: Set up the equation for the total weight of the mixture:
Total Weight = Weight of nuts costing $5 per kg + Weight of nuts costing $8 per kg
The weight of nuts costing $5 per kg is x kg.
The weight of nuts costing $8 per kg is y kg.
So, the equation becomes:
x + y = Total Weight
In this case, the total weight of the mixture is 10 kg, so the equation becomes:
x + y = 10
Step 4: Set up the equation for the average price of the mixture:
Average Price = Total Cost / Total Weight
The average price is given as $6 per kg, so the equation becomes:
6 = (5x + 8y) / 10
Now, you have a system of two equations:
5x + 8y = Total Cost
x + y = 10
You can solve this system of equations to find the value of x and y, which will give you the amount of each type of nut that should be mixed.