Question

The Coffee Counter charges $7.00 per pound for Kenyan French Roast coffee and $11.00 per pound for Sumatran coffeeHow much of each type should be used to make a 24 pound blend that sells for $9.00 per pound?The Coffee Counter should mix (blank) pounds of Kenyan Roast coffee and (blank) pounds of Sumatran coffee to make 24 pounds of a blend that sells$9.00 per pound?

Answer 1

Given:

The Coffee Counter charges $7.00 per pound for Kenyan French Roast coffee and $11.00 per pound for Sumatran coffee

Let the number of pounds from Kenyan French Roast coffee = x

And the number of pounds from Sumatran coffee = y

He wants to make a 24-pound blend that sells for $9.00 per pound

So, we have the following equations:

`\begin{gathered} x+y=24\rightarrow(1) \\ 7x+11y=9\cdot24\rightarrow(2) \end{gathered}`

From equation (1):

`x=24-y\rightarrow(3)`

substitute with (x) from equation (3) into equation (2) then solve for (y)

`\begin{gathered} 7\cdot(24-y)+11y=9\cdot24 \\ 7\cdot24-7y+11y=9\cdot24 \\ 4y=9\cdot24-7\cdot24 \\ 4y=2\cdot24 \\ y=(2\cdot24)/(4)=12 \end{gathered}`

substitute with (y) into equation (3) to find (x)

`x=24-12=12`

so, the answer will be:

The Coffee Counter should mix (12) pounds of Kenyan Roast coffee and (12) pounds of Sumatran coffee.