Let x be the number of quarters and y be the number of nickels in the piggy bank;
Since there are 63 coins in the piggy bank, then we have;
[tex]x+y=63\ldots\ldots\ldots\text{.. equation 1}[/tex]
Also, 20nickels is 1 dollar and also 4 quarters is 1 dollar.
Since there is $12.55 in the piggy bank, we have;
[tex]\frac{1}{4}x+\frac{1}{20}y=12.55\ldots\ldots\ldots\ldots\text{.equation 2}[/tex][tex]\begin{gathered} \text{From equation 1;} \\ y=63-x\ldots\ldots\ldots\ldots\text{equation 3} \end{gathered}[/tex]
Then, we substitute equation 3 in equation 2, we have;
[tex]\begin{gathered} \frac{1}{4}x+\frac{1}{20}(63-x)=12.55 \\ \text{Multiply through by 20} \\ 5x+63-x=251 \\ 4x=251-63 \\ 4x=188 \\ x=\frac{188}{4} \\ x=47 \end{gathered}[/tex]
Hence, the number of quarters in the piggy bank is 47
