Mark O. answered • 01/28/15

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This is a typical mixture problem. Let's say that the owner uses x lbs of the richer blend coffee at $9/lb. Then, to make 30 lbs of coffee, he would use 30 - x lbs of the cheaper coffee which is at $5/lb. He wants to choose the mixture such that he makes a blend that is worth $6.50/lb. He would write the following set-up equation:

($9/lb)(x lb) + ($5/lb)(30 - x lb) = ($6.50/lb)(30 lbs)

Notice that lbs cancel in every term of the equation. Essentially, the unit for each term of the equation is dollars.

So,

9x + 5(30 - x) = (6.50)(30)

9x + 150 - 5x = 195

Subtract 150 from each side of the equation and combine your x terms.

4x = 45

Divide both sides by 4. You get

x = 45/4 = 11.25 lbs

So, to make 30 lbs of a blend of coffee worth $6.50/lb, the owner would need to mix 11.25 lbs of the expensive coffee and 30 - 11.25 = 18.75 lbs of the cheaper coffee.