A newspaper carrier has $1.80 in change. He has two more quarters than dimes but three times as many nickels as quarters. How many coins of each type does he have?
[latex]1\ quarter=\$0.25\\1\ dime=\$0.10\\1\ nickel=\$0.05\\\\q\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ quarters\\d\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ dimes\\n\ \ \ \rightarrow\ \ \ the\ number\ of\ the\ nickels\\\\q=2d\ \ \ and\ \ \ n=3q\ \ \ \Rightarrow\ \ \ n=3\cdot 2d=6d\\\\q\cdot0.25+d\cdot0.10+n\cdot 0.03=1.80\\\\2d\cdot0.25+d\cdot0.1+6d\cdot0.05=1.8\\\\[/latex]
[latex]0.5d+0.1d+0.3d=1.8\\\\0.9d=1.8\ \ \ \Rightarrow\ \ \ d=2\ \ \ \Rightarrow\ \ \ q=2\cdot2=4\ \ \ and\ \ \ n=6\cdot2=12\\\\Ans.\ 4\ quarters,\ 2\ dimes,\ 12\ nickels[/latex]