A store manager wishes to reduce the price on her fresh ground coffee by mixing two grades. If she has 35 pounds of coffee which sells for $2.40 per pound, how much coffee worth $1.80 per pound must she mix with it so that she can sell the final mixture for $2.10 per pound?

Quick way:

$2.10 is $0.30 less than $2.40 and $0.30 above $1.80, I. E. half-way.

So the mix is equal amounts, or 17.5 lbs of each.

General way:

Let x be the percentage of $1.80 coffee, then 1-x is the percentage of $2.40 coffee.

To sell at $2.10, we have

$1.80x+$2.40 (1-x) = $2.10

Solve for x

$2.40-$2.10 = ($2.40-$1.80) x

=>

x=0.5, (1-x) = 1-0.50=0.5.

Hence 17.5 lbs of each of $2.40 and $1.80 coffee.