As the tax assessor for Indian Creek County, you have been informed that due to budgetary demands, a tax increase will be necessary next year. The total market value of the property in the county is $$400,000,000.$ Currently, the assessment rate is $35\%$ and the tax rate is $30$ mills. The county commission increases the assessment rate to $45\%$ and the tax rate to $35$ mills.

$($a$)$ How much property tax $($in $ $)$ was collected under the old rates?

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$($b$)$ How much more tax $($in $$)$ revenue will be collected under the new rates?

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