A coffee merchant combines coffee costing $6.50 per pound with coffee costing $4.00 per pound. How many pounds of each should be used to make 50 lb of a blend costing $4.90 per pound?

Answer 1

This problem essentially boils down to a system of two equations with two unknowns.

Let x = # of pounds of $6.50/lb coffee

Let y = # of pounds of $4.00/lb coffee

From the problem statement, we know we are making a 50 lb blend of coffee. We can write our first equation as follows:

x + y = 50

Next, we know the combined blend costs $4.90 per pound. So in a 50 lb bag, the total cost is:

(50 lb) x ($4.90/lb) = $245

This total cost is split between the $6.50/lb coffee and $4.00/lb coffee, but we don't know exactly how it is split yet. We can write our second equation to describe this split in terms of our variables.

($6.50)*x + ($4.00)*y = $245

Solving the first equation for y, we get:

y = 50-x

Now substitute this into the second equation:

($6.50)*x + ($4.00)*(50-x) = $245

($6.50)*x + $200 - ($4.00)*x = $245

($2.50)*x = $45

x = 18 lbs of $6.50/lb coffee

Substitute "x" into the first equation to solve for y:

y = 50-x

y = 50 - 18

y = 32 lbs of $4.00/lb coffee