solve using a system of equations

Question

The grocer has some $4-per-lb coffee and some $8-per-lb coffee that he will mix to make 50lb of $5.60-per-lb coffee. How many pounds of each should be used?(Hint: make a table with #of lbs, price/lb and total value)

Answer 1

Table:

 

Name            Amount      $(rate)

$4 coffee           x               $4        =   4x

$8 coffee           y               $8        =   8y

Mixture             50             $5.60    =   280

 

Equations:

x + y = 50

4x + 8y = 280

 

I'm going to multiply the first equation by -4 and then add the two equations together.

-4(x + y = 50) = -4x -4y = -200

 

    -4x -4y = -200

+  4x + 8y = 280

 

            4y = 80

              y = 20

 

And if y = 20, then x = 30 because x + y = 50.

 

So you will need 30 lbs of the $4 coffee and 20 lbs of the $8 coffee.