[tex]Let \: x \: be \: the \: money \: the \: Millers \: spent \\
The \: Rigbys \: spent:x-100 \\
The \: Smiths \: spent:2x \\
We \: have \: an \: equation:x + x - 100 + 2x = 580 \\ < = > 4x = 680 \\ < = > x = 170 = > 2x = 340 \\ So \: the \: Smiths \: spent \: \$340[/tex]