Results 1 to 12 of 12

Math Help - more problems..

  1. #1
    Newbie
    Joined
    Jul 2007
    Posts
    15

    Question more problems..

    find positive integers x,y,z such that 28x+30y+31z=365



    use exact calculation (no calculators or decimals allowed) to decide which is larger:
    (a) 28% of 75 or 75% of 28? (b) 76% of 27 or 57% of 36?



    the 1st July is a beautiful date, since the shortened form of the year number is equal to the product of the day number and the month number. 1.7.70. how many years in the 21st century have no beautiful dates at all?




    there are more but some have diagrams so i cannot type them out,,

    thanks u soo much!! xxxx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    find positive integers x,y,z such that 28x+30y+31z=365
    Solve for one of the variables, say z.
    z = \frac{365 - 28x - 30y}{31}

    Now we need to find an x, y pair such that the numerator is divisible by 31. There is an advanced method to help you with this, but the simplest thing to do is guess and check:
    (x, y) = (1, 1) \implies z = \frac{301}{31}

    (x, y) = (1, 2) \implies z = \frac{277}{31}

    etc.

    I get
    (x, y) = (1, 4) \implies z = 7

    A less trivial version:
    (x, y) = (2, 1) \implies z = 9

    I believe this covers the entire solution set.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    use exact calculation (no calculators or decimals allowed) to decide which is larger:
    (a) 28% of 75 or 75% of 28? (b) 76% of 27 or 57% of 36?
    a)
    28 \% = \frac{28}{100} = \frac{7}{25}

    75 \% = \frac{75}{100} = \frac{3}{4}

    So 28% of 75 is:
    \frac{7}{25} \cdot 75 = 7 \cdot 3 = 21
    and
    75% of 28 is
    \frac{3}{4} \cdot 28 = 3 \cdot 7 = 21

    So they are equal.

    The others are done the same way.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    the 1st July is a beautiful date, since the shortened form of the year number is equal to the product of the day number and the month number. 1.7.70. how many years in the 21st century have no beautiful dates at all?
    I don't understand. 1.7.70. The year is 70, the day is 1 and the month is 7. But 1 \cdot 7 \neq 70??

    (Now October 7th, 1970 ==> 7.10.70 works.)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2007
    Posts
    15

    Smile

    im still a little confused but thank you SO SO SO SO SOOO much for taking your time to help me you must be some mathematical genius to get it that quickly!!
    thanks xx
    ps. how old r u???????
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2007
    Posts
    15
    sorry i meant 1.7.07 typing error
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    im still a little confused but thank you SO SO SO SO SOOO much for taking your time to help me you must be some mathematical genius to get it that quickly!!
    thanks xx
    ps. how old r u???????
    Not a genius. Just been doing this for a while and I have a nice calculator to help me through the rough spots.

    For the record, I'll be 37 in August. (sobs)

    -Dan
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jul 2007
    Posts
    15
    28 \% = \frac{28}{100} = \frac{7}{25}

    75 \% = \frac{75}{100} = \frac{3}{4}

    So 28% of 75 is:
    \frac{7}{25} \cdot 75 = 7 \cdot 3 = 21
    and
    75% of 28 is
    \frac{3}{4} \cdot 28 = 3 \cdot 7 = 21

    So they are equal.

    The others are done the same way.



    how did you get:
    So 28% of 75 is:
    \frac{7}{25} \cdot 75 = 7 \cdot 3 = 21
    and
    75% of 28 is
    \frac{3}{4} \cdot 28 = 3 \cdot 7 = 21
    ???????????????????????
    please help! thanks xx
    -mich xxx
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    May 2007
    Posts
    237
    Quote Originally Posted by mich13 View Post
    find positive integers x,y,z such that 28x+30y+31z=365


    Do you remember how many months have 31, 30 and 28 days in a year?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    28 \% = \frac{28}{100} = \frac{7}{25}

    75 \% = \frac{75}{100} = \frac{3}{4}

    So 28% of 75 is:
    \frac{7}{25} \cdot 75 = 7 \cdot 3 = 21
    and
    75% of 28 is
    \frac{3}{4} \cdot 28 = 3 \cdot 7 = 21

    So they are equal.

    The others are done the same way.



    how did you get:
    So 28% of 75 is:
    \frac{7}{25} \cdot 75 = 7 \cdot 3 = 21
    and
    75% of 28 is
    \frac{3}{4} \cdot 28 = 3 \cdot 7 = 21
    ???????????????????????
    please help! thanks xx
    -mich xxx
    28% is the same as \frac{28}{100} which is the same as:
    \frac{28}{100} = \frac{4 \cdot 7}{4 \cdot 25} = \frac{7}{25}

    Thus to find 28% of a number we multiply it by \frac{7}{25}. 28% of 75 becomes:
    \frac{7}{25} \cdot 75 = \frac{7 \cdot 75}{25} = \frac{7 \cdot 3 \cdot 25}{25} = 7 \cdot 3 = 21.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,887
    Thanks
    326
    Awards
    1
    Quote Originally Posted by mich13 View Post
    use exact calculation (no calculators or decimals) to decide which is larger:
    76% of 27 or 57% of 36?



    PLEASE HELP I HAVE BEEN TRYING SO HARD BUT I CANNOT DO IT!!!!!




    pleeeeasssssse!
    thanks xxx
    76% is \frac{76}{100} = \frac{19}{25}

    So 76% of 27 is:
    \frac{19}{25} \cdot 27 = \frac{19 \cdot 27}{25}

    57% is \frac{57}{100}

    So 57% of 36 is:
    \frac{57}{100} \cdot 36 = \frac{57 \cdot 36}{100} = \frac{57 \cdot 9 \cdot 4}{25 \cdot 4} = \frac{57 \cdot 9}{25}

    So which is bigger?
    \frac{19 \cdot 27}{25} or <br />
\frac{57 \cdot 9}{25}?

    They are both over the same denominator, so the question becomes which numerator is bigger?
    19 \cdot 27 = 19 \cdot (3 \cdot 9)
    or
    57 \cdot 9 = (3 \cdot 19) \cdot 9?

    Again we see that the two are equal since the factors are the same.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Jul 2007
    Posts
    15

    Exclamation ..

    i get them all now, thanks! but i still dont understand the 'beautiful date' question... or how to do it!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 3rd 2011, 05:35 AM
  2. binomial problems/normal problems
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 19th 2010, 11:46 PM
  3. binomial problems as normal problems
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 19th 2010, 11:41 PM
  4. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 05:39 PM
  5. 2 Problems, need help, story problems!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 23rd 2007, 10:43 PM

Search Tags


/mathhelpforum @mathhelpforum