Let x be the number of nickels.
We know that we have one more than three times as many dimes as nickels, the number of nickels can be express as:
[tex]3x+1[/tex]We also know that she has five times as many quartes, this can be express as:
[tex]5x[/tex]Now, we also know that in total she has $41.70 then we have the equation:
[tex]0.05x+0.1(3x+1)+0.25(5x)=41.70[/tex]Solving for x we have:
[tex]\begin{gathered} 0.05x+0.1(3x+1)+0.25(5x)=41.70 \\ 0.05x+0.3x+0.1+1.25x=41.70 \\ 1.6x+0.1=41.70 \\ 1.6x=41.70-0.1 \\ 1.6x=41.6 \\ x=\frac{41.6}{1.6} \\ x=26 \end{gathered}[/tex]Now that we have the value of x we can plug it in the expression for the number of each type of coin.
For the nickels we have:
[tex]3(26)+1=79[/tex]For the dimes we have:
[tex]5(26)=130[/tex]Therefore we have 26 nickels, 79 dimes and 130 quartes.
