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Let there are x number of nickels and y number of quarters.
Total coins are 52, so first equation is,
[tex]\begin{gathered} x+y=52 \\ y=52-x \end{gathered}[/tex]The worth of nckel is 0.05$ and worth of quarter is 0.25$.
The worth for the nickels and quarter is $9. So the second equation is,
[tex]0.05x+0.25y=9[/tex]Substitute the value of y in the equation to obtain the value of x.
[tex]\begin{gathered} 0.05x+0.25(52-x)=9 \\ 0.05x+13-0.25x=9 \\ x=\frac{-4}{-0.20} \\ =20 \end{gathered}[/tex]Substitute 20 for x in the equation y=52-x to obatin the value of y.
[tex]\begin{gathered} y=52-20 \\ =32 \end{gathered}[/tex]So number of nickels is 20 and number of quarters is 32.