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Math Help - More Coins

  1. #1
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    More Coins

    Craig has $6.65 in nickels and dimes on his desk in a jar. If he has 11 less nickels than dimes, how many of each coin does he have?

    MY WORK:

    Let 5n = nickels

    Let 10d = dimes

    Then 5n + 10d = 665....This is the first equation.

    This is where I got stuck.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by magentarita View Post
    Craig has $6.65 in nickels and dimes on his desk in a jar. If he has 11 less nickels than dimes, how many of each coin does he have?

    MY WORK:

    Let 5n = nickels

    Let 10d = dimes

    Then 5n + 10d = 665....This is the first equation.

    This is where I got stuck.
    You used n nickel and d dimes
    Code:
    he has 11 less nickels than dimes,
    Using this we get another equation that

    d-11 = n

    There are two equation and two unknowns you can go ahead
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  3. #3
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    yes but...

    Quote Originally Posted by ADARSH View Post
    You used n nickel and d dimes
    Code:
    he has 11 less nickels than dimes,
    Using this we get another equation that

    d-11 = n

    There are two equation and two unknowns you can go ahead
    I read that we must assign the value of the coins to the variables representing the coins. For example, dimes would be 10d.

    Is the second equation d = n - 11 or 10d = 5n - 11?
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by magentarita View Post
    I read that we must assign the value of the coins to the variables representing the coins. For example, dimes would be 10d.

    Is the second equation d = n - 11 or 10d = 5n - 11?
    Lets see the complete answer

    We consider that we have n nickel coins and d dimes coin

    We than worked out that the total amount of money (a dime means 10 cents & a nickel coin means 5 cents) we have will be given by


    10d (from dime coins) + 5n(from nickel coins) = 665 cents
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    But according to second condition
    the number of nickel coins is less than number of dime coins by 11
    Hence

    d(no. of dime coins) -11= n(no. of nickel coins)

    ~~~~~~~~~~~~~~~~~~~~~~~~~

    Thus the second equation we get is

    d -11 = n
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  5. #5
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    Quote Originally Posted by magentarita View Post
    I read that we must assign the value of the coins to the variables representing the coins. For example, dimes would be 10d.

    Is the second equation d = n - 11 or 10d = 5n - 11?
    You understand, don't you, that "dimes would be 10d" makes no sense at all! Especially since you haven't said what "d" represents.

    In other words, write in full, grammatically correct, sentences. What you mean to say is "Let d be the number of dimes and n the number of nickels. Then the value of the coins is 10d for the dimes and 5n for the nickels."

    Yes, the fact that he has $6.65 in nickels and dimes means 10d+ 5n= 665.

    You are also told, "he has 11 less nickels than dimes", or n= d- 11. Solve those [b]two[b] equations for n and d.
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  6. #6
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    thanks

    Quote Originally Posted by ADARSH View Post
    Lets see the complete answer

    We consider that we have n nickel coins and d dimes coin

    We than worked out that the total amount of money (a dime means 10 cents & a nickel coin means 5 cents) we have will be given by

    10d (from dime coins) + 5n(from nickel coins) = 665 cents
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    But according to second condition
    the number of nickel coins is less than number of dime coins by 11
    Hence

    d(no. of dime coins) -11= n(no. of nickel coins)

    ~~~~~~~~~~~~~~~~~~~~~~~~~

    Thus the second equation we get is

    d -11 = n
    Thanks for breaking down the question.
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  7. #7
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    thanks

    Quote Originally Posted by HallsofIvy View Post
    You understand, don't you, that "dimes would be 10d" makes no sense at all! Especially since you haven't said what "d" represents.

    In other words, write in full, grammatically correct, sentences. What you mean to say is "Let d be the number of dimes and n the number of nickels. Then the value of the coins is 10d for the dimes and 5n for the nickels."

    Yes, the fact that he has $6.65 in nickels and dimes means 10d+ 5n= 665.

    You are also told, "he has 11 less nickels than dimes", or n= d- 11. Solve those [b]two[b] equations for n and d.
    Thank you for breaking down the question.
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