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Question of counting of coins

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Poll closed Sep 21, 2005.
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  1. Sep 19, 2005 #1
    This question seems easy, but I don't understand what it's mean with "without making change". Could someone help me?

    If you have 2 dollars, 2 quarter and 3 nickels:

    a) how many different sums can you pay without making change?

    b) Change the quarters into dimes and answer again.
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    This question is in a book and the answers are:
    a)35 (0 sum being excluded);
    b)23
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    To the item (a), I did this way:
    if it can to be used [0,1 or 2] dollars, [0,1 or 2] quarters and [0,1,2, or 3] nickels, then there are 3x3x4 = 36 - 1 = 35 different sums, excluding the 0 sum.
    Is my reasoning correct?
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    I don't find the answer to item (b). Could you help me ?
     
  2. jcsd
  3. Sep 19, 2005 #2

    NateTG

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    The tricky part for (b) is, of course, that 2 Nickels = 1 Dime. Perhaps you can find a different, easier set of coins that will generate the same sums as 2 dollars, 2 dimes, and 3 nickels?
     
  4. Sep 19, 2005 #3
    I didn't understand yet

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    I am trying, but I still don't obtaining the answer to part (b). Do you know how to do this ?
     
  5. Sep 19, 2005 #4

    EnumaElish

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    In this context "without making change" means:

    1. using up all the coins and getting no money back from the seller,

    and

    2. not exchanging any coins with coins of the same aggregate value but of different individual values. (e.g. you are not allowed to replace 1 Real with four 0.25 Reals.)
     
    Last edited: Sep 19, 2005
  6. Sep 19, 2005 #5

    EnumaElish

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    Part (b) is asking "how would your answer to part (a) be modified if we took away the two 0.25 Reals and gave you five 0.10 Reals?" (Now you have 2 dollars, 5 dimes and 3 nickels.)
     
  7. Sep 19, 2005 #6

    EnumaElish

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    Seems correct to me.
     
  8. Sep 19, 2005 #7

    NateTG

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    Your problem is that the nickels and dimes intersect, right?

    Let's try an easier version:

    How many different sums can you make with 7 nickels?
    How many different sums can you make with 3 dimes and 1 nickel?
     
  9. Sep 20, 2005 #8
    Using 2 dimes and 3 nickels,all the amonts within 1 dollar thar can be paid are
    0c,5c,10c,15c,20c,25c,30c,35c which is 8
    So when combined with $ it is
    8*3-1(exclude 0$)=23
     
  10. Sep 20, 2005 #9
    Thanks

    Thanks, I understood and I could response this question!!!
     
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