# A stack of nickel and dimes is worth $2.55. How do you find the number of nickels if the number of dimes is less than twice the number of nickels? ##### 1 Answer Feb 28, 2016 #### Answer: The number of nickels could be any odd number between 11 and 51 inclusive. #### Explanation: If $n$is the number of nickels and $d$is the number of dimes: $n$must be odd Since $2.55 can not be made up from an even number $\times 0.05$ plus any number $\times 0.10$

If $d = 0$ then $n = 51$
If $d = 1$ then $n = 49$
if $d = 2$ then $n = 47$
...and so on

We are told that $d < 2 n$ but this only places an lower limit on $n$:
$\textcolor{w h i t e}{\text{XXX}}$Since $5 n + 10 d = 255$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow n + 2 d = 51$
$\textcolor{w h i t e}{\text{XXX}}$and since $2 n > d$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow n + 4 n > 51$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 5 n > 51$
$\textcolor{w h i t e}{\text{XXX}}$and since $n$ must be an integer
$\textcolor{w h i t e}{\text{XXX}} \rightarrow n \ge 11$