Amerchant has coffee worth $60 a pound that she wishes to mix with 50 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. how many pounds of the & 60 coffee should be used?

  100 lbs

Step-by-step explanation:

Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...

  60x + 90·50 = 70(x+50)

  60x +4500 = 70x +3500 . . . . simplify

  1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x

  100 = x . . . . . . . . . . . . . . . . . . . divide by 10

The merchant should use 100 pounds of the $60 coffee.

The cost of the mix parts and the total mix is figured from ...

  (dollars/lb)×(lbs) = dollars

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50