If Julie has $1.25 in dimes and nickels, how many different combinations of the coins could she have?

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- Feb 1st 2010, 01:51 PMsri340algebra (combinations)
If Julie has $1.25 in dimes and nickels, how many different combinations of the coins could she have?

- Feb 1st 2010, 05:39 PMTheEmptySet
- Feb 1st 2010, 05:42 PMSoroban
Hello, sri340!

Quote:

Julie has $1.25 in dimes and nickels.

How many different combinations of the coins could she have?

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

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

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

So we have:

. . . $\displaystyle \begin{array}{|c|c|} \hline

\text{Dimes} & \text{Nickels} \\ \hline

0 & 25 \\ 1 & 23 \\ 2 & 21 \\ 3 & 19 \\ \vdots & \vdots \\ 10 & 5 \\ 11 & 3 \\ 12 & 1 \\ \hline\end{array}$

There are 13 combinations.