If Julie has $1.25 in dimes and nickels, how many different combinations of the coins could she have?
Hello, sri340!
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.