Question 313546: What is 50(N^2)? That is my original question.
I am trying to create a proff for a number trick.
this is what I have so far.
example
Choose a number 2
multipy it by 2 2(2)= 4
then add 5 4+5= 9
multiply by 50 50(9)= 450
add 1760 450+1760= 2210
subtract 1980 2210-1980= 230
My Proof:
N
2N
2N+5
50(2N+5)=100N+250
100N+250+1760= 100N+2010
100N+2010-1980= 100N+30
I am stuck after this point. The example answer is correct. I am suppose to end up with the original number plus my age and I did. Now, considering that I already know what N is my proff is actually still correct but it is incomplete and I don't know what to do from here. The idea is that it should work if any number was used. I assume my final proff should look something like this N and 30 with N representing 200 although it is really supposed to just be 2.
I want to show you the original problem.
PROBLEM:
1) Choose a number from 1 to 7, which represents the number of times you would like to eat dinner out each week (one per day).
2) Multiply this number by two.
3) Then add five.
4) Multiply this result by 50.
5) Now, if you have had your birthday this year already, add 1760 to the result in step 4. If not, add 1759
6) Then subtract your birth year.
The resulting number is a three-digit number. The first (leftmost) digit gives the number of times you would like to eat out each week. The other two give your current age.
INSTRUCTIONS: What I am supposed to do is:
1) Do a couple of examples with different numbers of dinners to get the feel of the process; Show these in your answer.
2) Construct a formal, “symbolic,” deductive reasoning proof for it, as seen in class with other problems (like we did with the number tricks) where you will introduce symbols and (a VERY small amount of) algebra along with your reasoning.
3) This is NOT a computation problem only, but mostly it is. It is not difficult, but you will need to play around with it.
4) You need to explain and show in mathematical terms clearly how and why the three-digit number gives you the dinner and the age.
5) I suggest that you use N for the number of dinners, and 19xy for your birth year. Be sure to clearly and specifically state how your age develops in the answer as the last two digits and why/how the number of dinners is first. This is where the credit is earned in particular.
I am on question 2, simply trying to create my proff. I hope that you can help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! My Proof:
N
2N
2N+5
50(2N+5)=100N+250
100N+250+1760= 100N+2010
100N+2010-1980= 100N+30
I am stuck after this point. The example answer is correct. I am suppose to end up with the original number plus my age and I did. Now, considering that I already know what N is my proff is actually still correct but it is incomplete and I don't know what to do from here. The idea is that it should work if any number was used. I assume my final proff should look something like this N and 30 with N representing 200 although it is really supposed to just be 2.
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Your proof is fine.
You ended up with 100N+30
Since N is a number between 1 and 7 100N is the hundreds digit of
a three-digit number where the 1st digit is the number of dinners
and the combination of the 2nd and 3rd digit is you age.
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If your N is 2, your final number will be 230.
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3) This is NOT a computation problem only, but mostly it is. It is not difficult, but you will need to play around with it.
You have done this in answering #2
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4) You need to explain and show in mathematical terms clearly how and why the three-digit number gives you the dinner and the age.
When you multiplied N by 100 you moved the number of dinners to the hundreth
place of a three-digit number.
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5) I suggest that you use N for the number of dinners, and 19xy for your birth year. Be sure to clearly and specifically state how your age develops in the answer as the last two digits and why/how the number of dinners is first. This is where the credit is earned in particular.
---
Try it with the "N" and the 19xy as your birth year so you can see how
the rest of the numbers simply concel themselves.
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Cheers,
Stan H.
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