\(x-\ number\ of\ quarters\\ y\ number\ of\ dimes\\\\quarters=0.25\$\\
dimes=0.1\$\\\\
\left \{ {{x+y=111} \atop {0.25x+0.1y=18.3}} \right. \\\\
x=111-y\\\\
0.25(111-y)+0.1y=18.3\\\\
27.75-0.25y+0.1y=18.3\\\\
-0.24y+27.75=18.3\ \ \ \ | subtract\ 27.75\\\\
-0.15y=-9.45\ \ \ | divide\ by\ -0.15\\\\
y=63\\\\
x=111-63=48\\\\ There\ were\ 63\ dimes\ and\ 48\ quarters.\)
