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age problem

 marleen is 3 years older than Ned and 2 years younger than Carla.  10 years ago Carla's age was equal to the sum of the ages of Ned and Marleen. How old is each now?

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Bethann D. | Mathematics, SAT, and General TutorMathematics, SAT, and General Tutor
5.0 5.0 (152 lesson ratings) (152)
To be able to fully answer this question, you must write an equation from the word problem. Be sure to look out for words such as and, less, more, etc. to signify what mathematical symbol (-, +, *, /) you need to use in your equation.
To begin with, let's say that Marleen's age is given by x, since she is the person in the middle. If Marleen=x, then Ned could be represented by three less than x. How would you write that algebraically? Also, if Marleen=x, then Carla would be 2 more than x. How would you write that algebraically?
Hopefully you came up with these answers:
From here, we can discuss the second part of the question. If Carla's age ten years ago was equal to the age of Ned and Marleen, how can this be shown in algebraic form?
To start, we know that Carla's age equals something, so Carla= or x+2=
Then, we write what it equals. You should end up with an equation from here.
To solve the equation, use basic algebraic techniques.
If you need help with these techniques, please let me know. Also, make sure that you refer back to the question and find out how old they are now rather than how old they were ten years ago.
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
4.8 4.8 (13 lesson ratings) (13)
Let M=Marleen's age
Marleen is 3 years older than Ned so Ned is 3 years younger than Marleen
Let M-3=Ned's age
Marleen is 2 years younger than Carla so Carla is 2 years older than Marleen
Let M+2=Carla's age
10 years ago means to subtract 10 years from each person's age
M-10=Marleen's age 10 years ago
M-3-10=Ned's age 10 years ago
M+2-10=Carla's age 10 years age
Carla's age=Ned's age + Marleen's age (10 years ago !)
15=M, Marleen's age
M-3=15-3=12, Ned's age
M+2=15+2=17, Carla's age
check:15-10=5, 12-10=2, 17-10=7, and 7=5+2
Marleen is 15
Ned is 12
Carla is 17


While your work is correct, you can skip the part about subtracting ten to eliminate confusion. The ages of the kids will have the same differences regardless of whether it occurs five years from now or ten years ago. The only thing you must remember after solving for x is to add values with ten in order to get the overall ages. You can do it either way. However, please do not give direct answers to students. It is appreciated. Thanks!
   Changing the time, 5 years ago, 5 years from now, etc will change the entire problem. Also, almost all of the tutors on this site do the problems out for the students. The students ask for the solution because they can't do a particular problem. They may have done twenty similar problems but just can't do this one that they are asking about. This is my format and, with all due respect, I am not going to change. What is the sense of posting a problem if nobody will do it ? I completely understand what you are saying because  I taught mathematics for 33 years.
The student has to understand how to go about setting up a problem in order to solve it. Practice makes perfect. This is why we give homework. However, some students just get stuck on a particular problem and need to see the entire solution done out. Hopefully, seeing the problem done out completely will add to the student's repertoire of problem solving strategies. The next time he/she sees a similar problem, the student will fall back on the solution that the teacher gave. If a student keeps asking for the same type of problem over and over again, tutors will usually comment on this.
Arthur, with all due respect...first, just because almost all the tutors around here just give the answer is not an excuse.  I'm not using it as an excuse, and I'm not going to let that influence me.  (And perhaps it's only the tutors who hang around here who do that.  How do you know about the rest of the 1000's of tutors here?)
What's the sense of posting a problem if nobody will do it?  Giving some explanation, a start, a basic setup, can all help the student without necessarily working through the whole thing - some students can understand with just that as well.  But no one bothers to try that.  I understand the need to see one worked through all the way, but an example would work for that, without doing their actual work for them.  Does anyone bother to try that?  What about asking to see the students' attempts first? There are many sites out there that have very strict rules on just answering the problem, so it's not like this is some novel idea, and it does work for those sites to not just solve things for students.
I really don't have much issue with doing one problem for someone if that's really all they ask, as long as the explanation for the steps is there.  But I have never seen one comment from anyone when a student keeps posting the same type of thing over and over.  There are students who post 10 questions every single day, and I've seen students who just come back and post the same question when I've presented a perfectly good example - i.e. the same problem with different numbers.
Since this unfortunately is attached to a student's post, and also unfortunately there is no PM system for us to use, I invite you to join our thread on the Forums to discuss this issue.  If you honestly believe you are right, you should have no issue presenting your argument there.