In 2010 a city raised $5,999,400 in tax revenue by charging each taxpayer the same amount. For 2011 there has been a net loss of 12 taxpayers, necessitating an increase fo $200 per taxpayer in order to maintain the tax revenue of $5,999,400. How many taxpayers were there in 2010?
X-Taxpayers in 2010.
(X - 12)Taxpayers in 2011.
$200(X - 12) = $5,999,400.
X - 12 = 29997 Taxpayers in 2011.
X - 12 = 29997,
X = 30009 Taxpayers in 2010.
To solve this problem, we need to set up an equation based on the given information and then solve for the unknown variable, which represents the number of taxpayers in 2010.
Let's denote the number of taxpayers in 2010 as "x".
According to the given information, the tax revenue in 2010 was $5,999,400, and each taxpayer was charged the same amount. Therefore, we can set up the equation:
Tax revenue / Number of taxpayers = Amount charged per taxpayer
$5,999,400 / x = Amount charged per taxpayer
Now, we are told that in 2011 there was a net loss of 12 taxpayers. This means that the new number of taxpayers in 2011 is (x - 12). We also know that to maintain the same tax revenue of $5,999,400, the amount charged per taxpayer had to increase by $200. Therefore, we can set up another equation based on this information:
Tax revenue / Number of taxpayers in 2011 = New amount charged per taxpayer
$5,999,400 / (x - 12) = (Amount charged per taxpayer in 2010 + $200)
Now, we can substitute the first equation into the second equation to eliminate "Amount charged per taxpayer":
$5,999,400 / (x - 12) = ($5,999,400 / x + $200)
Next, we can cross multiply and solve for x:
$5,999,400 * x = ($5,999,400 + $200 * (x - 12))
$5,999,400 * x = $5,999,400 + $200x - $2400
$5,999,400 * x - $200x = $5,999,400 - $2400
$5,999,200 * x = $5,997,000
x = $5,997,000 / $5,999,200
x ≈ 999
Therefore, there were approximately 999 taxpayers in 2010.