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Math Help - algebra (combinations)

  1. #1
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    algebra (combinations)

    If Julie has $1.25 in dimes and nickels, how many different combinations of the coins could she have?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by sri340 View Post
    If Julie has $1.25 in dimes and nickels, how many different combinations of the coins could she have?
    Setting up the relationship we get

    .25Q+.05N=1.25 \iff 25Q+5N=125

    Now lets isolate N to get

    5N=125-25Q \iff N =25-5Q \iff N=5(5-Q)
    Now just plug in in Q=0,1,2,3,4,5 to get all of the ordered pairs.
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    Hello, sri340!

    Julie has $1.25 in dimes and nickels.
    How many different combinations of the coins could she have?

    Let: . \begin{array}{ccc} d &=& \text{no. of dimes} \\ n&=&\text{no. of nickels} \end{array}


    Then: . \begin{array}{c}d\text{ dimes have a value of }10d\text{ cents} \\ n\text{ nickels have a value of }5n\text{ cents}\end{array}

    Their total value is 125 cents: . 10d + 5n \:=\:125 \quad\Rightarrow\quad n \:=\:25 - 2d


    So we have:

    . . . \begin{array}{|c|c|} \hline<br />
\text{Dimes} & \text{Nickels} \\ \hline<br />
0 & 25 \\ 1 & 23 \\ 2 & 21 \\ 3 & 19 \\ \vdots & \vdots \\ 10 & 5 \\ 11 & 3 \\ 12 & 1 \\ \hline\end{array}


    There are 13 combinations.

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