Need help on 8th grade math problem!

Discussion in 'Chit Chat' started by TwinMa, Apr 1, 2009.

  1. TwinMa

    TwinMa New Member

    Anybody good with word problems? This is from my daughter's 8th grade math homework and I'm drawing a blank on how to do it. Here it is:

    A math test has 2 problems. The first was solved by 70% of the students. The second was solved by 60% of the students. Every student solved at least one of the problems. 9 students solved both problems. How many students took the test?

    If you figure it out, please tell me how you did it, too! Thanks!
  2. TwoCatDoctors

    TwoCatDoctors New Member

    This to me sounds so much like some trick question. Wouldn't all the students in the class take the test, or 100 percent??
  3. rockgor

    rockgor Well-Known Member

    I have no problems with such tests. That's because test taking is all behind me.

    The answer appears to be 30 students.

    I solved it the old-fashioned way. I looked it up. Haha

  4. Rafiki

    Rafiki New Member

    I think you're going to need an x. You may also need a y and even a z, who knows! In grade 8 you may only need an x but it's been a very long time since I was in grade 8 - obviously! Put the 9 over the x and see what happens. The 60 and 70 should probably go over 100s and there will be some of these: =. One of those (=) goes right before the answer so that should help.

    I wouldn't share this with you except that I see Rock has already cheated the answer for you. That's no fun! Mess around with x's for a while before you look it up.

    I'm really, really glad I'm not taking grade 8 math!!!

  5. gapsych

    gapsych New Member

    However, I used to teach 8th grade math, even though I am not certified to teach math!! Long story, but was very good with math in high school and college. However, I preferred the social sciences.

    If I could not come up with the correct answer from the teacher's guide, I would ask one of the students who did get the answer, to show the class it was done. They never figured out that I did not know the answer, LOL!!

    At least I think?

    I learned a lot of math this way as the process of getting an answer is sometimes as important as the answer.


    ETA However, since I am right brained and depending on how you read the question, I would have counted the answer that they all took the test, as correct.

    [This Message was Edited on 04/01/2009]
  6. TwinMa

    TwinMa New Member

    Rock - how did you find that on the internet? Did you just google the whole question? Whatever you did, it was quite resourceful!

    But I still don't get how they solved it. I don't understand what they are defining as "x". Their logic doesn't make sense to me. Even if you assume 30 is the correct answer, I don't see how you can go back to the original problem and make it work.

    70% of 30 is 21, so 21 kids would have gotten Ques 1 right
    60% of 30 is 18, so 18 kids would have gotten Ques 2 right

    But how do you prove that 9 kids got both questions right? And what difference does it make that every student solved at least one problem? Arrgh!

    Thanks to everyone for trying!
  7. TwinMa

    TwinMa New Member

    We must have been posting at the same time.

    You said you got the right answer (30, right?). How did you come up with that?
  8. rockgor

    rockgor Well-Known Member

    I think I searched for: math test, 70%, 60%, 9 students.

    Found the answer on page four. Could not, however, understand the process of solving the puzzle.

    This seems to be an algebra problem. You have an unknown number (X) and you need to find it. That's
    the definition of algebra to me.

    I had algebra in the 9th grade and found it highly confusiatin'.

    When I did a lot of editing and proofreading at the law firm, I found most of our attorneys
    couldn't do simple arithmetic, much less algebra.

    Doubt you'll ever need to solve such a problem again.


  9. gapsych

    gapsych New Member

    Actually, I just copied the person who got the correct answer. Now I am curious how you really get the answer.

    This was my weird version of an April Fools Day joke which I was going to reveal later. Yeah right. I was!! I was!!


    [This Message was Edited on 04/01/2009]
  10. TwinMa

    TwinMa New Member

    That's the funny part. My other twin daughter had this same math problem about a year ago, and I couldn't figure it out then, either. I asked someone at work and she solved it with no problem (she's a math genius). However, I couldn't follow her logic. Something about two overlapping circles with 9 being in the part that overlaps. I figured I didn't really need to "get it" because I'd never see a problem like that again.

    Well, lo & behold, here it is--again! I'll ask her--again--tomorrow, and I'm sure I won't get it--again!
  11. springwater

    springwater Active Member

    Do you chat in any chat groups like msn or yahoo / google?

    I remember i once asked help for my daughters math problem in a chat room and after a lot of no gos i finally got one gentleman to help...he worked it out and daughter...of course she had to be there because i know next to nothing about math. I can say the multiplicatin tables upto 12 and do simple addition subtraction but thts it, and i am so relieved to know from Rock that even lawyers attorneys dont know math. Makes me fel less stupid.

    God Bless
  12. gapsych

    gapsych New Member

    As Dave Barry would say, I am not making this up. The answer I got is 4.354.....

    I am going to solve this, even if it drives me crazy.

    Is your daughter in an accelerated math class? My class was for kids whose skills in math were below normal but IQ's were normal or above. Hence, I did not need to be certified. Bottom line: They were desperate for a teacher.

  13. TwinMa

    TwinMa New Member

    I don't do any other groups--I'm exclusive to ProHealth ChitChat!

    After a bit of further research, I found that the overlapping/intersecting circles are called Venn diagrams. But I still don't know how exactly to use it for this problem. I'll find out tomorrow from my co-worker. I'll definitely share what I find out!

    gapsych - 4.354 students! lol. No accelerated math class. One daughter (the one I'm helping tonight) is in pre-Algebra. The other one is in regular Algebra. Both are in 8th grade. The one who had the problem last year can't remember how we solved it and I threw away the notes (how unlike me)!

    Here is another answer I got from googling the entire problem:
    The overlap is 30% so you know that 30% solved both problems and 9 students solved all problems
    3 students are 10% so there are 30 students.

    I'm still not seeing it. Time for bed. I give up for tonight.

  14. gapsych

    gapsych New Member

    I looked where Rock got the answer and this is the explanation that I think makes the best sense.

    TwinMa, Your explanation of the overlapping circles helped me understand how you get the answer but not all the way.

    I did not get the correct answer but did get to 1.3 before messing up.How I got to that point I don't remember. When I read how you solve the problem after this I am throughly confused and get one. Maybe someone else could elaborate?

    Hope this makes sense to you.

    Let x = total number of students who took the exam.
    Let y = number of students who did problem A
    Let z = number of students who did problem B

    x = y + z - 9 (because 9 students did both problems, so there is an overlap in y and z)

    Rearrange equation for x:
    x = y + z - 9
    x + 9 = y + z

    .7x = y (70% of total students = number of students who did A)
    .6x = z (60% of total students = number of students who did B)

    Add these two equations together to get:
    1.3x = y + z

    Set the two equations equal to eachother (y + z = y + z):
    x + 9 = 1.3x

    Solve for x:
    9 = .3x

    x = 30

    30 students did the exam.

    Let's check:
    Problem A:
    y = .7x = .7(30) = 21
    Problem B:
    z = .6x = .6(30) = 18

    y + z = 21 + 18 = 39
    y + z = x + 9 = 30 + 9 = 39
    [This Message was Edited on 04/01/2009]
  15. alaska3355

    alaska3355 New Member

    Good job, Gap! This is similar to stuff my boys are working on, but I was glad to see it solved.
    Sometimes these are real headscratchers!
  16. TwinMa

    TwinMa New Member

    Brilliant, brilliant, brilliant! Thank you gapsych! Did you come up with all that?

    I think I get it now. I'll see if my co-worker can get to the same place in a different way.

    I actually like the answer TwoCatDoctors gave, too. How many students took the test: 100% lol.

    Thanks everyone for all the help!
  17. gapsych

    gapsych New Member

    As much as I would like to take credit, I went to the site Rock mentioned and cut and paste the above. I thought I said this however, by the time I posted it, I was on sensory overload from trying to figure out the problem.

    I think I should get an A+ for stealing this off the site Rock mentioned. Sometimes, even in math you have to be creative. LOL

    Houston, do we have another problem?


  18. rockgor

    rockgor Well-Known Member

    guys still blithering on over this problem?

    I love the answer 4.354. It's so precise. And since we know 9 students got both answers right, it's
    so obviously wrong. Smiling out loud.

    Anyhoo, we had Venn diagrams in Introduction to Logic 101. Imagine two circles that overlap.
    This creates 3 areas. The center area is shaped like a marquis diamond. Label the areas A,B, and C.

    Now you can use the diagram to check a syllogism.

    John is a man.
    Some men are redheads.
    Therefore, John may be a redhead.

    Label one circle A for men, one circle B for redheads. The overlapping area is men who are
    redheads. We can't tell from the limited info if John is in that area or not; he may be.

    Logic should be taught in high school. Be a good thing if people learned how to identify fallacious
    arguments by salesmen, politicians, etc.

    I wonder how many kids figured out the math problem.


  19. gapsych

    gapsych New Member

    Your logic is faulty. I know a man named John who is bald, LOL!

    Since some people think one person's logic is another's illogical thinking, do you think this statement applies to the lawyers you worked with?

    I agree thinking skills are very important and unfortunately are neglected by our schools. These skills will carry you far. Sometimes as far as Australia if you have enough bonus points from the airline.

  20. rockgor

    rockgor Well-Known Member

    Jean! Even if it's not right, it certainly looks right to me.

    In summary then, 30% or 9 students got A plus, The overlap (or Phar lap) came in first, John
    is a bald redhead, and I wonder if they still teach that new math nowadays.

    So, are we finally done w/ this problem, or is it like Fermat's last theorem, destined to be with us forever?