You have one type of nut that sells for $2.40/lb and another type of nut that sells for $6.60/lb. You would like to have 12.6 lbs of a nut mixture that sells for $6.10/lb. How much of each nut will you need to obtain the desired mixture?
To solve this problem, let's assign variables to the unknown amounts of each type of nut. Let's call the amount of the $2.40/lb nut "x" lbs, and the amount of the $6.60/lb nut "y" lbs.
Now, let's set up an equation based on the given information:
2.40x + 6.60y = 6.10(12.6)
This equation represents the total cost of the mixture, where the left side represents the cost of the $2.40/lb nut and the $6.60/lb nut, and the right side represents the cost of the desired mixture.
Next, we can simplify the equation:
2.40x + 6.60y = 76.86
To solve for x and y, we need another equation. In this case, it will be an equation representing the total weight of the mixture:
x + y = 12.6
Now, we have a system of equations:
2.40x + 6.60y = 76.86 (Equation 1)
x + y = 12.6 (Equation 2)
To solve this system of equations, we can use either substitution or elimination method. In this case, let's use the substitution method.
Rearrange Equation 2 to solve for x:
x = 12.6 - y (Equation 3)
Substitute Equation 3 into Equation 1:
2.40(12.6 - y) + 6.60y = 76.86
Now, simplify and solve for y:
30.24 - 2.40y + 6.60y = 76.86
4.2y = 46.62
y = 11.1
Now that we have the value of y, substitute it back into Equation 3 to solve for x:
x = 12.6 - 11.1
x = 1.5
Therefore, to obtain the desired mixture, you will need 1.5 lbs of the $2.40/lb nut and 11.1 lbs of the $6.60/lb nut.