[tex]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.
[/tex]
