The vendor of a coffee cart mixes coffee beans that cost $8 per pound with coffee beans that cost $4 per pound. How many pounds of each sould be used to make a 60-pound blend that sells for $5.25 per pound?
$8 coffee __________
$4 coffee __________
Work with the total cost of each part of the mix. They have to add up the the final cost. So, if there are x lbs of $8 coffee, the rest (60-x) has to be the $4 coffee.
8x + 4(60-x) = 5.25(60)
x = 18.75
CAN YOU GIVE ME A FORMULA FOR THIS
To solve this problem, we can use the method of setting up a system of equations.
Let's assume the number of pounds of $8 coffee beans used is x, and the number of pounds of $4 coffee beans used is y.
x + y = 60 (equation 1) - This equation represents the total weight of the mixture, which is 60 pounds.
8x + 4y = 5.25 * 60 (equation 2) - This equation represents the total cost of the mixture, which is the cost per pound ($5.25) multiplied by the weight (60 pounds).
Now we can solve this system of equations.
Using equation 1, we can solve for x:
x = 60 - y
Substituting this value of x into equation 2, we get:
8(60 - y) + 4y = 5.25 * 60
Simplifying the equation:
480 - 8y + 4y = 315
Combining like terms:
480 - 4y = 315
Subtracting 480 from both sides:
-4y = -165
Dividing both sides by -4:
y = 41.25
Now we can substitute this value into equation 1 to find x:
x + 41.25 = 60
x = 18.75
Therefore, the vendor should use 18.75 pounds of $8 coffee beans and 41.25 pounds of $4 coffee beans to make a 60-pound blend that sells for $5.25 per pound.
$8 coffee = 18.75 pounds
$4 coffee = 41.25 pounds
To find the number of pounds of each type of coffee bean needed, we can set up a system of equations based on the given information.
Let's assume x represents the number of pounds of $8 coffee beans and y represents the number of pounds of $4 coffee beans.
From the problem, we know:
1) The total weight of the blend is 60 pounds. So, we have the equation: x + y = 60.
2) The average cost of the blend is $5.25 per pound. The cost of each type of coffee beans is the weight of that type multiplied by its unit cost. Therefore, we have the equation: (8x + 4y)/60 = 5.25.
Now we can solve the system of equations to find the values of x and y.
Let's start with the first equation:
x + y = 60
To make it easier, let's solve for x:
x = 60 - y
Now, substitute x in the second equation with 60 - y:
(8(60 - y) + 4y)/60 = 5.25
Simplifying the equation:
(480 - 8y + 4y)/60 = 5.25
Combine like terms:
(480 - 4y)/60 = 5.25
Cross-multiply:
480 - 4y = 5.25 * 60
Simplify further:
480 - 4y = 315
Rearrange the equation:
4y = 480 - 315
Calculating:
4y = 165
Now, divide both sides by 4:
y = 165/4
Simplifying:
y = 41.25
Now, substitute the value of y back into x = 60 - y:
x = 60 - 41.25
x = 18.75
So, to make a 60-pound blend that sells for $5.25 per pound, the vendor should use:
$8 coffee: 18.75 pounds
$4 coffee: 41.25 pounds