A distributor needs to mix some Terraza coffee that normally sells for $9.00 per pound with some Kona coffee that normally sells for $13.50

Question

A distributor needs to mix some Terraza coffee that normally sells for $9.00 per pound with some Kona coffee that normally sells for $13.50 per pound to create 50 pounds of a mix that can sell for $9.54 per pound. How many pounds of each kind of coffee should they mix?

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Thông Đạt 1 year 2021-08-31T14:44:50+00:00 1 Answers 0 views 0

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    2021-08-31T14:46:41+00:00

    Answer:

    Step-by-step explanation:

    Mixture problems are really easy because the table never varies from one problem to another and they don’t have a lot of variations in them like motion problems do. The table for us will look like this, using T for Terraza coffee and K for Kona:

                    #lbs     x       $/lb       =         Total

    T

    K

    Mix

    Now we just have to fill this table in using the info given. We are told that T coffee is $9 per pound, and that K coffee is $13.50 per pound, so we will fill that in first:

                     #lbs        x        $/lb       =        Total

    T                                           9

    K                                         13.50

    Mix

    Next we are told that the mix is to be 50 pounds that will sell for $9.54 per pound

                      #lbs      x       $/lb        =        Total

    T                                         9

    K                                       13.50

    Mix              50                 9.54

    Now the last thing we have to have to fill in this table is what goes in the first column in rows 1 and 2. If we need a mix of 50 pounds of both coffees and we don’t know how many pounds of each to use, then under T we have x and under K we have 50 – x. Notice along the top we have that the method to use to solve this problem is to multiply the #lbs by the cost per pound, and that is equal to the Total. So we’ll do that too:

                     #lbs       x       $/lb      =      Total

    T                   x        x          9         =        9x

    K             50 – x      x       13.50     =    675 – 13.50x

    Mix            50        x         9.54     =     477

    The last column is the one we focus on. We add the total of T to the total of K and set it equal to the total Mix:

    9x + 675 – 13.5x = 477 and

    -4.5x = -198 so

    x = 44 pounds. This means that the distributor needs to mix 44 pounds of T coffee with 6 pounds of K coffee to get the mix he wants and to sell that mix for $9.54 per pound.

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