How many of the cheaper coffee beans with be needed for the mixture?

Question

A store has two types of coffee beans. The first type sells for $5.20/lb, the second for $5.80/lb. How many pounds of the first type must be mixed with 5lbs of the second to produce a blend selling for $5.35/lb?

Answer 1

If we have x pounds of the $5.20 per pound coffee

added to 5 pounds of the $5.80 then our result is

(x+5) pounds of $5.35 per pound coffee

 

5.2x + 5.8(5) = 5.35(x+5)

5.2x + 29 = 5.35x + 26.75

5.2x - 5.35x = 26.75 - 29

-0.15x = - 2.25

 

x = -2.25/-0.15

 

x = 15 pounds