Question

Suppose Ken has 25 coins and nickels and dimes only and has a total of a $1.65 how many of each coin does he have?

Answer 1

$x-\ number\ of\ nickels\\ y-\ number\ of\ dimes\\\\ x+y=25 \ \ \ | x=25-y\\ 0.05x+0.1y=1.65\\\\ 0.05(25-y)+0.1y=1.65\\\\ 1.25-0.05y+0.1y=1.65\\\\ 1.25+0.05y=1.65\ \ \ | subtract\ 1.25\\\\ 0.05y=0.4\ \ \ \ \ | divide\ by\ 0.05\\\\ y=8\\\\ x=25-8=17\\\\ There\ are\ 17 \ nickels\ and\ 8\ dimes.$