Word problem

Question

a coffee shop owner decided to blend a gourmet brand of coffee with a cheaper brand. the gourmet coffee usually sells for $9.00/lb. the cheaper brand sells for $5.00/lb. how much of each type should he mix in order to have 30 lb of coffee that is worth $6.50/lb

Answer 1

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.