Results 1 to 9 of 9

Math Help - SAT Question

  1. #1
    Junior Member
    Joined
    Jul 2011
    Posts
    25

    Inequality question

    For how many ordered pairs of positive integers (x,y) is 2x+3y<6

    1
    2
    3
    5
    7
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2011
    Posts
    15

    Re: Inequality question

    Quote Originally Posted by RK29 View Post
    For how many ordered pairs of positive integers (x,y) is 2x+3y<6

    1
    2
    3
    5
    7
    (0, 0)
    (0, 1)
    (1, 0)
    (1, 1)
    (2, 0)

    I count 5.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2011
    Posts
    25

    Re: Linear equation question

    Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jul 2011
    Posts
    25

    Re: Inequality question

    Quote Originally Posted by rdtedm View Post
    (0, 0)
    (0, 1)
    (1, 0)
    (1, 1)
    (2, 0)

    I count 5.
    so did I but the answer key is it's 1
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2011
    Posts
    15

    Re: Inequality question

    Quote Originally Posted by RK29 View Post
    so did I but the answer key is it's 1
    Answer key is wrong - I have seen many errors in test prep books when I tutor confused students.. Answer has to be five unless it was transcribed wrong
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Jul 2011
    Posts
    25

    Re: Inequality question

    okay thanks

    Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2011
    Posts
    15

    Re: Linear equation question

    Quote Originally Posted by RK29 View Post
    Line l passes through origin and is perpendicular to the line 4x+y=k, where K is constant. If the two lines interesect at ( t, t+1), what is the value of t?
    Passes through origin means line has form y= mx, where m is some real number.

    Rearranging the perpendicular line, we get y = -4x + k, so this line has a slope of -4, so the inverse reciprocal slope is 1/4.
    Which means, Line 1 has an equation of y = (1/4)x

    Line 1: y = (1/4)x
    Line 2: y = -4x + k

    Since we know they intersect at (t, t+1), this must be a solution to both equations. Since Line 2 would have infinite solutions (since k is unknown), we choose Line 1 to solve for t.

    t+1 = (1/4)t
    1 = (-3/4)t
    (-4/3) = t

    So, t = -4/3
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,646
    Thanks
    1596
    Awards
    1

    Re: Inequality question

    Quote Originally Posted by RK29 View Post
    For how many ordered pairs of positive integers (x,y) is 2x+3y<6
    1, 2, 3, 5, 7
    the answer key is it's 1
    Quote Originally Posted by rdtedm View Post
    Answer key is wrong - I have seen many errors in test prep books when I tutor confused students.. Answer has to be five unless it was transcribed wrong
    The answer key is correct.
    There is only one pair of positive integers that works: (1,1).
    @ rdtedm, you should that 0 is not a positive integer.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,736
    Thanks
    642

    Re: Inequality question

    Hello, RK29;669895!

    \text{For how many ordered pairs of }positive\text{ integers }(x,y)\text{ is }2x+3y \,<\, 6

    . . (a)\,1 \qquad (b)\;2 \qquad (c)\;3 \qquad(d)\;5 \qquad (e) 7

    For positive integers, there is one pair: (1,1)


    Code:
          |
         2*
          |  *
         1+   ♠ *
          |        *
      - - + - + - + - * - -
          |   1   2   3
          |
    Ah, Plato beat me to it . . .
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum