Math

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A coffee dealer mixed 12 pounds of one grade coffee with 10 pounds of another grade of coffee to obtain a blend worth $54. He then made a second blend worth $61 by mixing 8 pounds of the first grade with 15 pounds of the second grade. Find the price per pound of each grade.

  • Math -

    first grade ---- x lbs
    2nd grade ----- y lbs

    12x + 10y = 54 ---> 6x+5y = 27
    8x + 15y = 61

    1st equation times 3
    18x + 15y = 81
    8x + 15y = 61
    subtract them
    10x = 20
    x = 2
    sub back into 6x+5y=27
    12+5y=27
    y = 3

    1st grade is $2 per pound, 2nd grade is $3 per pound

    (coffee at $2 a pound!!! WOW, time to update that texbook)

  • Math -

    define Variables,
    Grade#1=x
    Grade#2=y
    total cost=z
    a=pounds of Grad#1
    b=pounds of Grade#2
    write equation,
    z=ax+by
    Define values
    12 pounds Grade1 and 10 pounds of Grade2 worth $54; 8 pounds Grade1 and 15 pounds Grade2 worth $61
    Plug in values, isolate one variable,
    54= 12x+10y , 61= 8x+15y
    -12x=-12x , -8x=-8x
    54-12x=10y , 61-8x=15y
    (54-12x)/10=(10y)/10 , (61-8x)/15=
    (54-12x)/10x=y , (15y)/15
    (27-6X)/5=y , (61-8x)/15=y
    set equations equal to each other, solve for remaining variable,
    (27-6x)/5=(61-8x)/15
    *15=*15
    3(27-6x)=61-8x
    81-18x=61-8x
    +18x= +18x
    81=61+10x
    -61=-61
    20=10x
    (20)/10=(10x)/10
    2=y
    Pick one equation, Plug in new value, solve for last variable,
    54=12x+10y
    54=12x+10*(2)
    54=12x+20
    -20= -20
    34=12x
    (34)/12=(12x)/12
    (17/6)=x
    2.83=x

    Grade one is $2/lb
    Grade two is $2.83/lb

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