MATH 112 helpl please

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Bill brought four times as may apples as harry and three times as may apples as martin. If Bill, and martin purchased less than a total of 190, apples, what is the greatest number of apples that bill could have purchased?

  • MATH 112 helpl please -

    apples for Harry -- x
    apples for Bill --- 4x
    apples for Martin -- y
    but Bill's apples = 3 times Martin
    4x = 3y
    y = 4x/3

    Bill + martin < 190
    4x + 4x/3 < 190
    times 3
    12x + 4x < 570
    16x < 570
    x <35.6
    4x < 142.5
    greatest number of apples for Bill is 142

    but Bill bought 4 times as many as Harry, and we will assume that there were no fractional apples .
    Thus Bill's number of apples should be a multiple of 4
    and the greatest such multiple which is less than 142
    is 140
    BUT, that would still give Martin partial apples
    how about 136?
    then y = (4/3)(136) --- still not a whole number
    how about 132 ???
    then y = (4/3)(132) = 44 and x = 3y/4 = 33

    yeah, whole apples all around

    Harry --- 33 apples
    Bill ----- 132 apples
    Martin --- 44 apples

    Notice ratio of
    Harry : Bill : Martin = 33 : 132 : 44 , where 132 + 44 < 190
    = 3: 12: 4

    if we went for the ratio of
    36 : 144 : 48 , the sum of apples for Bill and Martin > 190
    even though the relationship of apples between them would be correct

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