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Math Help - Can't figure out how the answer was arrived at :(

  1. #1
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    Can't figure out how the answer was arrived at :(

    I have a couple questions that I know the solutions to, but I can't for the life of me figure out the process involved at arriving at those solutions...

    1) If 18*sqrt(18) = r*sqrt(t), where t and r are positive integers and r > t, which of the following could be the value of r*t? (solution is 108)

    2) The eggs in a certain basket are either white or brown. If the ration of the number of white egges to the number of brown eggs is (2/3), each of the following could be the number of eggs in the basket EXCEPT:

    a) 10
    b) 12 (this is the answer)
    c) 15
    d) 30
    e) 60

    I thought about proportionalities with problem 1 and got no where, and with problem 2 I thought I had it nailed until I checked the answer.

    As always, any advice is greatly appreciated
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  2. #2
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    Re: Can't figure out how the answer was arrived at :(

    these are not university-level algebra questions.

    for (1):

    since everything in sight is positive we can square both sides without fear.

    thus from:

    18√18 = r√t, we have:

    (324)(18) = r2t

    183 = 5832 = r2t.

    clearly t < 18, or else r2t > t3 > 5832. so t is some divisor of 18: 1,2,3,6,or 9.

    if t = 1, r = √(5832), which is not an integer.
    if t = 2, r = √(2916) = 54 <--this works ( (18)3/2 = (9)(18)2, which has square root 3*18 = 54).
    if t = 3, r = √(1944), not an integer
    if t = 6, r = √(972), not an integer
    if t = 9, r = √(648), not an integer

    (look at the prime factorization of 18 cubed)

    so the only case where r and t are integers with r > t is t = 2, r = 54, hence rt = 108.

    (2) 2x + 3x = 5x, the number of eggs in the basket must be a multiple of 5. 12 is not a multiple of 5.
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  3. #3
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    Re: Can't figure out how the answer was arrived at :(

    Thanks Denovo, and I just realized I was posting these questions in the incorrect place (my apologies to all, I see where to post these now). Thanks again for your help.
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