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Algebra

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An apple orchard charges a fixed amount for the first four bushels of apples purchased and an extra amount for each additional bushel purchased. If the cost of 11 bushels of apples is $33 and the cost of 19 bushels is $55, what is the fixed charge for the first four bushels of apples?

  • Algebra -

    fc + (11-4)*b = fc + 7*b = 33

    fc + (19-4)*b = fc + 15*b = 55

    where fc is the fixed charge of the first 4 bushels, and b is the price per bushel of each additional bushel over 4

    Use algebra to solve these two equations for b and fc:

    fc + 7*b = 33
    fc + 15*b = 55

  • Algebra -

    let
    cost = m(n-4) + b , where n is the number of bushels, b is the extra charge for the first 4 bushels and m is the cost per bushel
    so for 11 bushels, cost is 33
    33 = 7m + b
    so for 19 bushels, cost = 55
    55 = 15m + b
    subtract them
    22 = 8m
    m = 22/8 = 2.75
    sub into 33 = 7m+b
    33 = 19.25 + b
    b = 13.75

    the fixed cost is $13.75

    check:
    our equation would be
    cost = 2.75(n-4) + 13.75

    if n = 11, cost = 2.75(7) + 13.75 = 33
    if n=19, cost = 2.75(15) + 13.75 = 55 , YEAH

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