Results 1 to 10 of 10

Math Help - Word problems

  1. #1
    Member
    Joined
    Sep 2006
    Posts
    134

    Word problems

    Help please. Thanks!

    Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?

    If the larger of the two numbers which is 36 is divided by the smaller, the quotient is 3 and remainder is 3. What is the smaller number?

    The sum of two numbers is 52. If the ratio is 3/10, what are the numbers?
    That's all. Thanks!
    Last edited by reiward; October 8th 2006 at 12:39 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by reiward View Post
    Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?
    Jose does 1/20 of the work per day, his friend does 1/25 of the work per
    day. Together they do:

    1/20+1/25 = 9/100

    of the work per day, so they take 100/9=11.11 days to complete the work
    working together.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by reiward View Post
    If the larger of the two numbers which is 36 is divided by the smaller, the quotient is 3 and remainder is 3. What is the smaller number?
    larger/smaller=3 remainder 3

    theis means that

    larger = 3*smaller +3

    as the larger is 36, we have:

    36 = 3*smaller +3,

    so subtracting 3 from both sides:

    36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

    so

    33 = 3*smaller,

    and so smaller = 11.

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,185
    Thanks
    404
    Awards
    1
    Quote Originally Posted by reiward View Post
    The sum of two numbers is 52. If the ratio is 3/10, what are the numbers?
    That's all. Thanks!
    Let the two numbers be x and y.

    Thus x + y = 52
    and
    x/y = 3/10

    From the second equation we have
    10x = 3y

    y = (10/3)x

    Putting this into the first equation:
    x + (10/3)x = 52

    (13/3)x = 52

    x = (3/13)*52 = 12.

    Thus y = (10/3)x = (10/3)*12 = 40.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by reiward View Post

    Jose can do a piece of work in 20 days and his friend can do the same work in 25 days. How long will it take them to finish the work if they will work together?
    Here is a rule.

    If it takes a man "a" amount of time to do a work. And it takes a woman "b" amount of time to do a work. Then it takes,
    ab/(a+b)
    Amount of time to do it together.
    In your example,
    a=25 and b=20
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Sep 2006
    Posts
    134
    Quote Originally Posted by CaptainBlack View Post
    larger/smaller=3 remainder 3

    theis means that

    larger = 3*smaller +3

    as the larger is 36, we have:

    36 = 3*smaller +3,

    so subtracting 3 from both sides:

    36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

    so

    33 = 3*smaller,

    and so smaller = 11.

    RonL
    thanks, but how did that became "+3".. and why did you subtract 3 from both sides...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2006
    Posts
    134
    Quote Originally Posted by topsquark View Post
    Let the two numbers be x and y.

    Thus x + y = 52
    and
    x/y = 3/10

    From the second equation we have
    10x = 3y

    y = (10/3)x

    Putting this into the first equation:
    x + (10/3)x = 52

    (13/3)x = 52

    x = (3/13)*52 = 12.

    Thus y = (10/3)x = (10/3)*12 = 40.

    -Dan
    I cant understand.. How did that become 13/3 and then 3/13.. I knw the answers are correct but I can't understand the solutions...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by reiward View Post
    I cant understand.. How did that become 13/3
    You had: x+(10/3)x

    Rewrite: 1x+(10/3)x

    Rewrite again: (3/3)x+(10/3)x

    Add: [(3+10)/(3)]x

    thus: (13/3)x

    and then 3/13.. I knw the answers are correct but I can't understand the solutions...
    You had: (13/3)x=52

    now divide both sides by 13/3 to get: x=52/(13/3)

    but remember, to divide you multiply by the inverse of the fraction, thus: x=52*(3/13)
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Sep 2006
    Posts
    134
    Quote Originally Posted by Quick View Post
    You had: x+(10/3)x

    Rewrite: 1x+(10/3)x

    Rewrite again: (3/3)x+(10/3)x

    Add: [(3+10)/(3)]x

    thus: (13/3)x


    You had: (13/3)x=52

    now divide both sides by 13/3 to get: x=52/(13/3)

    but remember, to divide you multiply by the inverse of the fraction, thus: x=52*(3/13)
    oh i see, thanks!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by CaptainBlack View Post
    larger/smaller=3 remainder 3

    theis means that

    larger = 3*smaller +3

    as the larger is 36, we have:

    36 = 3*smaller +3,

    so subtracting 3 from both sides:

    36 - 3 = 33 = 3*smaller + 3 -3 = 3*smaller

    so

    33 = 3*smaller,

    and so smaller = 11.

    RonL


    Quote Originally Posted by reiward View Post
    thanks, but how did that became "+3".. and why did you subtract 3 from both sides...
    The +3 is the remainder that you are told exists.

    I subtract 3 from both sides as a long winded way of moving the +3 on the
    right over to become -3 on the left.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problems with integration word problems
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2010, 06:39 PM
  2. Word Problems
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 6th 2009, 01:01 PM
  3. Word Problems
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: September 22nd 2008, 11:06 AM
  4. 3 word problems
    Posted in the Algebra Forum
    Replies: 11
    Last Post: April 25th 2008, 09:31 PM
  5. Word Problems
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 23rd 2007, 01:34 PM

Search Tags


/mathhelpforum @mathhelpforum