how many pounds of cashew nuts that sell for 2.00 a pund should be mixed with peanuts, which sell for 80 cents a pound to make a 10 pound mixture that sells for 1.28 a pound
To solve this problem, we can set up a mixture equation.
Let's say x represents the amount of cashew nuts in pounds that need to be mixed with peanuts.
First, let's calculate the total cost of the cashew nuts: 2.00 * x
Next, let's calculate the total cost of the peanuts: 0.80 * (10 - x)
We subtract x from 10 because we know that the total mixture should weigh 10 pounds.
The total cost of the mixture is given as 1.28 * 10.
Since the total cost of the mixture is equal to the sum of the cost of the cashew nuts and the cost of the peanuts, we can set up the equation:
2.00 * x + 0.80 * (10 - x) = 1.28 * 10
Now we can solve for x:
2.00 * x + 0.80 * 10 - 0.80 * x = 1.28 * 10
2.00 * x + 8 - 0.80 * x = 12.8
1.20 * x = 12.8 - 8
1.20 * x = 4.8
x = 4.8 / 1.20
x = 4
Therefore, 4 pounds of cashew nuts that sell for $2.00 a pound should be mixed with peanuts to make a 10 pound mixture that sells for $1.28 a pound.
To find the number of pounds of cashew nuts that should be mixed with peanuts, we can follow these steps:
Step 1: Assign variables to the unknowns:
Let's assign the variable "x" to represent the number of pounds of cashew nuts we need.
Step 2: Write down the equation:
The equation can be formed by considering the total weight and the cost per pound of the mixture. The equation is:
(2.00 * x) + (0.80 * (10 - x)) = 1.28 * 10
Step 3: Solve the equation:
Simplify the equation step by step:
2.00x + 0.80(10 - x) = 1.28 * 10
2.00x + 8 - 0.80x = 12.80
1.20x + 8 = 12.80
1.20x = 12.80 - 8
1.20x = 4.80
x = 4.80 / 1.20
x = 4
So, 4 pounds of cashew nuts should be mixed with peanuts to make a 10-pound mixture that sells for $1.28 per pound.