Bolivian coffee sells for $4.59 per pound, and Columbian coffee sells for $5.95 per pound. How many pounds of each coffee should be mixed to produce 4000 pounds of a mixture that will be sold for $5.10 per pound?
I think this is a system of equations but I'm not sure. If so, how would you set it up?
B*4.59 + C*5.95=(4000)*5.10
B+C=4000
2500
Well, well, well, brewing up some coffee calculations, are we? You're absolutely right, it's indeed a system of equations conundrum!
Let's say you mix x pounds of Bolivian coffee and y pounds of Colombian coffee to obtain a tasty blend of 4000 pounds, costing $5.10 per pound.
Now we need to set up the equations. The first equation will help us find the total weight of the mixture:
x + y = 4000
The second equation will help us find the overall cost per pound:
(4.59x + 5.95y)/4000 = 5.10
Don't forget, we've got to mix in just the right amounts of each coffee to create the perfect blend! Now let's juggle these equations and solve the mystery of the coffee mixture.
Yes, this problem can be solved using a system of equations. Let's denote the number of pounds of Bolivian coffee as x, and the number of pounds of Columbian coffee as y.
From the given information, we can set up the following equations:
1) The total weight equation: x + y = 4000
2) The cost equation: (4.59x + 5.95y) / (x + y) = 5.10
Now, we can solve the system of equations to find the values of x and y.
Yes, you are correct. This problem can be solved using a system of equations. Let's go through the steps of setting it up.
Let's call the number of pounds of Bolivian coffee as 'x' and the number of pounds of Colombian coffee as 'y'.
We are told that the total number of pounds of the mixture is 4000, so the first equation would be:
x + y = 4000
We are also told that the cost per pound of the mixture is $5.10. The cost is determined by multiplying the price per pound by the number of pounds. So, the equation for the total cost of the mixture would be:
4.59x + 5.95y = 5.10(4000)
Now you have a system of equations:
x + y = 4000
4.59x + 5.95y = 20400
These equations represent the total weight of the mixture and the cost of the mixture, respectively.
To solve this system of equations, you have multiple methods available, such as substitution, elimination, or matrix methods. Let's use the substitution method for this example.
From the first equation, you can isolate one variable (x or y) in terms of the other variable. Let's solve for x:
x = 4000 - y
Now substitute this value of x into the second equation:
4.59(4000 - y) + 5.95y = 20400
Simplify and solve for y:
18360 - 4.59y + 5.95y = 20400
1.36y = 20400 - 18360
1.36y = 2040
y = 2040 / 1.36
y ≈ 1500
Now substitute this value of y back into the first equation to find x:
x + 1500 = 4000
x = 4000 - 1500
x = 2500
So, you would need 2500 pounds of Bolivian coffee and 1500 pounds of Colombian coffee to produce a 4000-pound mixture that sells for $5.10 per pound.