A health food store sells a mixture of raisins and roasted nuts. Raisins sell for $4.00/kg and nuts sell for $6.00/kg. How many kilograms of each should be mixed to make 40 kg of this snack worth $4.75/kg?
To determine the number of kilograms of raisins and roasted nuts needed to make a 40 kg mixture worth $4.75/kg, we can set up a system of equations.
Let's assume the weight of the raisins is x kg and the weight of the roasted nuts is y kg.
We know that the total weight of the mixture is 40 kg, so we have the equation:
x + y = 40 (Equation 1)
We also know the price per kilogram for the mixture is $4.75/kg. To calculate the total price of the mixture, we multiply the price per kilogram by the weight of each ingredient and sum them up. The total price can also be expressed as:
4.00x + 6.00y = (4.75)(40) (Equation 2)
Now we have two equations with two variables (x and y). We can solve this system of equations to find the values of x and y, representing the weight of raisins and roasted nuts, respectively.
To solve the system of equations, we'll use the method of substitution or elimination. Let's solve it using the substitution method:
From Equation 1, we can rewrite it as:
x = 40 - y
Substituting this value of x into Equation 2, we get:
4.00(40 - y) + 6.00y = (4.75)(40)
Now, we solve this equation for y:
160 - 4.00y + 6.00y = 190
Simplifying the equation gives:
2.00y = 190 - 160
2.00y = 30
y = 15
Using this value in Equation 1, we can find the weight of raisins:
x + 15 = 40
x = 40 - 15
x = 25
Therefore, to make a 40 kg mixture worth $4.75/kg, you would need 25 kg of raisins and 15 kg of roasted nuts.
Xdxd
the cost for the parts must add up to the cost for the mix, so
r+n = 40
4r+6n = 4.75*40