Lucy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lucy

Question

Lucy's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Lucy $5.95

per pound, and type B coffee costs $4.25

per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $411.40

. How many pounds of type A coffee were used?

Answer 1

Lacey, this is easily solved by using a system of two linear equations in two variables.

 

Our variables will be:

X = "Number of pounds of Coffee A"

Y = "Number of pounds of Coffee B"

 

Now we need to come up with the two equations relating these variables. We get these from your problem statement.

First, since we know that Coffee A costs $5.95 per pound and Coffee B costs $4.25 per pound, and the total cost for this month's blend was  $411.40, we have that:

5.95*X + 4.25*Y = 411.40

 

 

To simplify calculations, you can multiply both sides of this equation by 100, to get:

595*X + 425*Y = 41140          [1]

 

 

Now, since we know that this month's blend used three times as many pounds of Coffee B as it did of Coffee A, we have that:

Y = 3*X          [2]

 

Now, we can solve this system of equations [1] and [2] easily. For example, you can just use substitution, and replace Y = 3*X in equation [1], to get:

 

595*X + 425*(3*X) = 41140     [Replace Y with 3*X)

595*X + 1275*X = 41140         [Multiply]

1870*X = 41140                       [Add]

X = 41140 / 1870

X = 22

 

Therefore, 22 pounds of Coffee A were used.

 

I hope that helps you.