Question

A coffee mixture has beans that sell for $1.35 per pound and beans that sell for $1.05 per pound. If 120 pounds of beans create a mixture worth $1.15 per pound, how many pounds of each bean is used?

Answer 1

40 lb of $1.35/lb; 80 lb of $1.05/lb

Answer 2

Let e be the amount of 1.35 beans and c be the amount of 1.05 beans...

(1.35e+1.05c)/120=1.15 we know e+c=120, so e=120-c making the equation:

(1.35(120-c)+1.05c)/120=1.15

(162-1.35c+1.05c)/120=1.15

162-0.3c=138

-0.3c=-24

c=80, and since e=120-c, e=40 so:

80 lb of the $1.05 beans are mixed with 40 lb of the $1.35 beans to produce a 120 lb mixture worth $1.15 per pound.