Let

'x' = pounds of $5-per-pound coffee

'y' = pounds of $10-per-pound coffee

She will mix them to get 50 pounds of $6-per-pound coffee that is

x + y = 50 (she will mix both coffees and get total of 50 pounds of $6-per-pound coffee)

5*x + 10*y = 6*50 (total value of the coffee)

The solutions of the system gives the answer

x + y = 50

5*x + 10*y = 300

x = 40 pounds

y = 10 pounds

The grocer should use 40 pounds of $5-per-pound coffee and 10 pounds of $10-per-pound to make 50 pounds of $6-per-pound coffee.