The owner of the Fancy Food Shoppe wants to mix cashews selling at $8.00/kg and pecans selling at $7.00/kg. How many kg of each kind of nut should be mixed to get 8 kg worth $7.25/kg?
To solve this problem, we can use a system of equations. Let's assume that x represents the amount of cashews (in kg) and y represents the amount of pecans (in kg) needed to achieve the desired mixture.
First, we need to set up the equation based on the total weight of the mixture. Since we want to end up with 8 kg of nuts, we can write the equation:
x + y = 8 (Equation 1)
Next, we need to set up the equation based on the total cost per kilogram of the mixture. We want the mixture to be worth $7.25/kg, so we multiply the cost of cashews ($8.00/kg) by the amount of cashews (x) and the cost of pecans ($7.00/kg) by the amount of pecans (y), and add the two amounts. This gives us:
8x + 7y = 8 * 7.25 (Equation 2)
Now we have a system of equations that we can solve simultaneously. To do this, we can use the substitution or elimination method.
Let's solve this system of equations using the substitution method.
From Equation 1, we have:
x = 8 - y
Substituting this value of x into Equation 2:
8(8 - y) + 7y = 8 * 7.25
Simplifying the equation:
64 - 8y + 7y = 58
Combine like terms:
-y = -6
Dividing by -1:
y = 6
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
x + 6 = 8
x = 8 - 6
x = 2
Therefore, you would need 2 kg of cashews and 6 kg of pecans to get an 8 kg mixture worth $7.25/kg.