School-Safe Puzzle Games

A Unique Blend

A Cafe owner purchases 2 kinds of Kopi Luwak coffee beans-one at $320 per pound, and the other,  an even better quality, at $400 per pound. He mixes together some of each, and he plans on selling this mix at $430 per pound. In doing so, he plans to make a profit of 25%  on the cost. How many pounds of each kind of coffee must he use to make a mixture of a hundred pounds weight?

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9 Comments to “A Unique Blend”


  1. Shawn | PUZZLE GRANDMASTER | Profile

    70# of the $320/# beans & 30# of the $400/# beans


    If he buys X pounds of $320/# and Y pounds of $400/#, then:


    X + Y = 100#


    100# * $430/# = 1.25 * [($320/# * X) + ($400/# * Y)]


  2. Bobo The Bear | PUZZLE MASTER | Profile

    First, if $430 reflects cost plus profit (C+P), and his profit margin is 25% (P = .25C), then
    430 = (C + .25C)
    C = 344 = average cost per pound


    Now we use an equation for the combined costs
    320(x) + 400(100-x) = 344(100)
    x = 70


    He should use 70 lbs of the lesser quality coffee mixed with 30 lbs of the better quality coffee.


  3. John Lewis Highsmith | Profile

    This description may be a bit lengthy. I get into my teaching mode on this type problem and I make no apologies for that.


    We can set up 2 equations (these are known as simultaneous equations, since they deal with the same conditions.)


    Using the usual suspects, x and y, where x = the weight of the lower quality beans and y = the weight of the better quality, we have:


    x + y = 100 This is the weight relationship.


    320x + 400y = ? This is the cost relationship.


    The reason for the ? is that the cost is yet to be determined.


    A third equation is needed: C(ost) + P(rofit) = S(elling price), or, in this case C + 0.25C = 430 and C = 344/pound, for a total cost of 34400. Remember, the profit was set as 25% of the cost.


    This gives us the second equation as 320x + 400y = 34400.


    From here the procedure is:


    Multiply the first equation by -320 (or -400, if you wish), giving -320x – 320y = -32000. Needless to say, (but I will anyway, for the heedless) the equation will be different if you use -400, but the final results will be the same either way.


    Add this result to the second equation.


    320x + 400y = 34400
    -320x – 320y = -32000


    The x coefficient is 0 and we are left with the equation 80y = 2400, or y = 30.


    The result is 30 pounds of the better quality beans and 70 pounds of the “inferior” (if that word could be applied to this type coffee) beans.


    70*320 + 30*400 = 34400, 0.25*34400 = 8600, 34400 + 8600 = 43000, or 430/#


    And, as the Latins would have it “QED”.


  4. suineg | PUZZLE MASTER | Profile

    Ok, I think this could be the answer:
    X= Number of pounds of the 320$ coffee beans
    Y= Number of pounds of the 400$ coffee beans
    C= Cost of the mix
    Equations:
    1)320X + 400Y = C
    2)X + Y = 100


    You know that you have to make 25% of profit and you also know the total sale of the mix is 100* 430= 43000 because its 100 pounds of the mix sell at 430 per pound, cool.


    Now, the profit in this example is 25% of the cost is the (total sale) = 1,25C, but total sale is 43000 so: C= 43000/1.25 or C= 34400


    Now substitute C in (1) and solve the 2 equations:
    -80X = -5600; X= 70 so Y= 30


    Now lets check this: 70*320 + 30*400= 34400;
    43000-34400= 8600; 0.25*34400= 8600 , cool its verified so:
    the Mix should have: 70 pounds of the 320$ coffee bean and 30 pounds of the 400$ coffee bean


  5. Mashplum | PUZZLE MASTER | Profile

    70 pounds of the $320 coffee would cost $22,400, and 30 pounds at $400 would be $12,000. The 100 pounds of blend would cost the owner $34,000. $34,400 plus 25% ($8,600) is $43,000 or $430 per pound.


  6. Hex | PUZZLE MASTER | Profile

    70 and 30 pounds


  7. Mashplum | PUZZLE MASTER | Profile

    Click the link! THIS COFFEE IS MADE FROM POO!


  8. Chinadoll | Profile

    48lbs of each of the two coffees.


  9. bcrox | Profile

    70 pounds @320 plus 30 pounds @ 400 will give 100 pounds sold for 430 per pound will give a 25% profit


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