A store manager wants to mix two different brands of coffee to make 480 pounds to sell at $2.68 a pound. He uses a brand of coffee worth $2.50 a pound and another brand worth $2.80 a pound. How many pounds of each should be used?

Let's define:

X = number of pounds of the brand 1 (price = $2.50 per pound)

Y = number of pounds of the brand 2 (price = $2.80 per pound)

We want to make a mix of 480 pounds, then:

X + Y = 480.

And we want the mean price to be $2.68, then:

(X*$2.50 + Y*$2.80)/480 = $2.68

Then we have a system of equations:

X + Y = 480

(X*$2.50 + Y*$2.80)/480 = $2.68

To solve this, the first step will be to isolate one variable in one of the equations, and then replace this in the other equation.

Let's isolate X in the first eq.

X = 480 - Y.

Now we can replace this in the other equation and get:

((480 - Y)*$2.50 + Y*$2.80)/480 = $2.68

Now let's solve this for Y.

((480 - Y)*$2.50 + Y*$2.80) = $2.68*480 = $1,286.40

$1,200 + Y*$0.30 = $1,286.40

y*$0.30 =  $1,286.40 - $1,200 = $86.40

Y = $86.40/$0.30 = 288

Then:

X = 480 - Y = 480 - 288 = 192

Then the manager must use 192 pounds of the brand that costs $2.50 per pound, and 288 pounds of the brand that costs $2.80 per pound.

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