A grocer wants to mix two kinds of coffee. One kinds sells for $1.15 per pound, the other sells for $1.40 per pound. He wants to mix a total of 30 pounds and sell it for $1.35 per pound. How many pounds of each kind should he use in the new mix

Step-by-step explanation:

Let the amounts (weights) of the $1.15 mix and the $1.40 mix be c and d.

Then c + d = 30 lb. We can solve this for c, obtaining d = 30 - c.

The cost equation is ($1.15/lb) c + ($1.40/lb) d = ($1.35/lb) (30 lb)

Substituting 30 - c for d, we get:

($1.15/lb) c + ($1.40/lb) (30 - c) = ($1.35/lb) (30 lb). Solve this for c:

1.15c + 42.00 - 1.40c = 40.5.

Then - 0.25c = 40.5 - 42.0, or - 1.5.

Finally, - 0.25c = - 1.50. This yields c = 6.

If c = 6 lb, then (30 - 6) lb = d = 24 lb.

Need 24 lb of the $1.15/lb kind and 6 lb of the $1.40/lb kind.