Question

A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?

Answer 1

$x-\ number\ of\ dimes\\y-\ number\ of\ quarters\\\\ \left \{ {{x+y=250\ \ \ | x=250-y} \atop {0.1x+0.25y=39.25\ \ \ \ \ \ \ \ \ \ \ \ \ }} \right. \\\\ substitution\ method\\\\ 0.1(250-y)+0.25y=39.25\\\\ 25-0.1y+0.25y=39.25\\\\ 25+0.15y=39.25\ \ \ \ | subtract\ 25\\\\0.15y=14.25\ \ \ \ | divide\ by\ 0.15\\\\y=95\\\\x=250-95= 155\\\\ There\ are\ 155\ dimes\ and\ 95\ quarters.$