Put the number of nikels,dimes and quarters is:a,b,c

We have:\(\left\{{}\begin{matrix}a+b+c=37\\a-b=4\\c-a=2\end{matrix}\right.\)\(\Rightarrow\left(a+b+c\right)+\left(a-b\right)+\left(c-a\right)=43\)\(\Rightarrow a+2c=43\).

Because \(c-a=2\) so \(\left(a+2c\right)+\left(c-a\right)=45\Rightarrow3c=45\Rightarrow c=15\Rightarrow\left\{{}\begin{matrix}a=13\\b=9\end{matrix}\right.\)

Answer:The number of nickels is 13

              The number of dimes is:9

              The number of quarters is:15