Question

A city commission has proposed two tax bills. The first bill requires that a homeowner pay $1850 plus 3% of the assessed home value in taxes. The second bill requires taxes of $300 plus 8% of the assessed home value. What price range of home assessment would make the first bill a better deal?

Answer 1

To determine which tax bill is better, calculate when Bill 1's tax ($1850 + 0.03V) is less than Bill 2's tax ($300 + 0.08V) based on the home's assessed value (V). The equation shows that Bill 1 is a better deal for home assessments over $31,000.

Step-by-step explanation:

The question involves a comparison of two proposed property tax bills to determine which is more advantageous for homeowners based on their home's assessed value. Given the two proposed bills, let's clearly define the total tax for each bill based on the assessed home value (V).

Bill 1: Total Tax = $1850 + 0.03V

Bill 2: Total Tax = $300 + 0.08V

To find the price range of home assessments where Bill 1 is a better deal than Bill 2, we need to determine when the total tax from Bill 1 is less than the total tax from Bill 2:

$1850 + 0.03V < $300 + 0.08V

Subtracting 0.03V from both sides and $300 from both sides:

$1550 < 0.05V

Dividing both sides by 0.05:

V > $31,000

Therefore, for homeowners with a home assessed at a value greater than $31,000, Bill 1 would result in lower taxes than Bill 2.