A merchant has coffee worth $80 a pound that she wishes to mix with 70 pounds of coffee worth $70 a pound to get a mixture that can be sold for $75 a pound. How many pounds of the $80 coffee should be used?

10 lbs

Step-by-step explanation:

Amount of coffee of 20$/lb = x lb

Its cost = 20*x $

Cost of other coffee = 80*50=4000 $

Total amount of coffee = (x+50) lb

The final mixture costs = 70$/lb

Total cost of the mixture = (x+50) * 70

So,

We have the equation

(x+50) * 70=20*x + 4000

50*x = 500

x=10

So, amount of 20$/lb coffee = 10 lb