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If paint is sold for $ 15 a can and $20 a can and they sell 320 dollars worth of paint, how many cans of paint do they sell? I know it takes 7 cans of paint at 20 equaling 140 and 12 cans at 15 equaling 180 but I', stumped at how to write the equation

  • math -

    Let x = 15$ paint

  • math -

    Number of $15 cans --- x
    number of $20 cans --- y

    15x + 20y = 320
    divide by 5

    3x + 4y = 64

    we are looking at the equation of a straight line, where the solutions can only be integers, (can't buy a partial can of paint)
    x-intercept = 64/3 , x < 21
    y-intercept = 64/4 , y < 16

    3x = 64-4y
    x = (64-4y)/3
    64-4y must be a multiple of 3
    with y as an integer, 64-4y can only be
    60 56 52 48 44 40 36 32 28 24 20 16 12 8 4

    of those the only multiples of 3 are:
    60 48 36 24 and 12

    so, assuming they buy at least one of each can, possible solutions for (x,y) are
    (20,1)
    (16,4)
    (12,7) ---- your answer
    (8,10)
    (4,13)

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