Results 1 to 6 of 6

Thread: Algebra Problem

  1. #1
    5 Star Lounger
    Join Date
    Jan 2001
    Location
    La Jolla,CA
    Posts
    1,078
    Thanks
    12
    Thanked 36 Times in 35 Posts

    Algebra Problem

    (since the Geometry one was so easy)

    Each student in a group of 30 students studies German, Italian, or both. The total number of students studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?

  2. #2
    Platinum Lounger
    Join Date
    Nov 2001
    Location
    Melbourne, Victoria, Australia
    Posts
    5,016
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Algebra Problem

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Italian only = 6
    German only = 9
    Both = 15

    Looks like the "trick" is to use 3 unknown variables, not just the intuitive two.</span hide>

    Good problem!

    Alan

  3. #3
    5 Star Lounger
    Join Date
    Jan 2001
    Location
    La Jolla,CA
    Posts
    1,078
    Thanks
    12
    Thanked 36 Times in 35 Posts

    Re: Algebra Problem

    You are correct. However, did you use intuition or write the equations??

  4. #4
    Platinum Lounger
    Join Date
    Nov 2001
    Location
    Melbourne, Victoria, Australia
    Posts
    5,016
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Algebra Problem

    I guess I intuitively wrote the equations. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

    Alan

  5. #5
    Silver Lounger
    Join Date
    Mar 2001
    Location
    Dallas, Texas, USA
    Posts
    1,680
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Algebra Problem

    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">01 G+I+B = 30 : <font color=yellow>German + Italian + Both = 30</font color=yellow>
    02 G = I+3 : <font color=yellow>German = Italian + 3</font color=yellow>
    03 B = I + I+3 : <font color=yellow>Both = Italian + Italian + 3</font color=yellow>
    04 (I+3) + (I) + (I+I+3) = 30 : <font color=yellow>Substitutions for Line 01, Replace G and B with I.</font color=yellow>
    05 4I + 6 = 30 : <font color=yellow>Simplify</font color=yellow>
    06 4I = 24 : <font color=yellow>Subtract 6 from both sides...</font color=yellow>
    07 I = 6 : <font color=yellow>Divide both sides by 4 to solve I(Italian)</font color=yellow>
    08 G = 9
    09 B = 15</span hide>

  6. #6
    New Lounger
    Join Date
    Nov 2008
    Posts
    2
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Re: Algebra Problem

    I used only 2 variables.
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Since 15 student study both, G+I=15 and then G=I+3 so I+I+3=15 </span hide>
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">6 students take italian</span hide>

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •