1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Tricky word problem?

  1. Jun 8, 2016 #1
    I'm studying for the ACT and this was one of the practice test problems. The book does offer an explanation for how to get the answer but it isn't very detailed and I still don't know what I'm doing wrong.

    1. The problem statement, all variables and given/known data
    The larger of two numbers exceeds twice the smaller number by ##8##. The sum of twice the larger and ##3## times the smaller number is ##65##. If ##x## is the smaller number, which equation below determines the correct value of ##x##?

    A. ##3(2x+8)+2x=65##
    B. ##3(2x-8)+2x=65##
    C. ##(4x+8)+3x=65##
    D. ##2(2x+8)+3x=65##
    E. ##2(2x-8)+3x=65##​

    (According to the book, the correct answer is D.)

    2. Relevant equations

    To be consistent with the book, I'll let the larger number be ##y##, and the smaller number be ##x##.

    3. The attempt at a solution
    Taking this one step at a time:

    The larger of two numbers exceeds twice the smaller number by ##8##.
    I think this translates into ##y+8=2x##.

    The sum of twice the larger and ##3## times the smaller number is ##65##.
    So this means that ##2y+3x=65##. Now, because they want the answer to be in terms of ##x##, I need to rewrite ##y## in terms of ##x## (which is ##y=2x-8##) and plug that into the formula.

    Then it becomes ##2(2x-8)+3x=65##. This is answer option E, but apparently this is isn't the right answer.​

    Please, look over my steps and see if you can spot what I missed. The correct answer, D, differs only by the sign inside the parenthesis. I don't see what I'm doing wrong, and I'm really confused as to how they got ##+8##. Thank you.
     
  2. jcsd
  3. Jun 8, 2016 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If ##y## exceeds ##2x## by ##8## then ##y = 2x + 8##.
     
  4. Jun 8, 2016 #3
    Ohh... so I must've messed up at the first step then. I think I see what I did wrong now: to show that ##y## was greater than ##2x## by ##8##, I should have added the 8 on the other side of the equation. Dumb mistake on my part. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Tricky word problem?
  1. Tricky word problem (Replies: 1)

  2. Word problem (Replies: 6)

  3. Word problem (Replies: 3)

Loading...