Answer
The home must be valued at a price $greater$ $than$ $32,000$ $dollars$ for the first tax bill to be a better deal than the second tax bill.
Work Step by Step
To solve this exercise, we must first model the equations for both tax plans: $$Bill_{1} = 1,800 + 0.03V$$ $$Bill_{2} = 200 + 0.08V$$ where $V$ represents the value of the homes. Since we're interested in the amount of value that makes the first bill a better deal (i.e., $Bill_{1}$ is less than $Bill_{2}$), we can write this in the following manner: $$Bill_{1} \lt Bill_{2}$$ $$1,800 + 0.03V \lt 200 + 0.08V$$ where by solving for V: $$1,800 - 200 \lt 0.08V - 0.03V$$ $$1,600 \lt 0.05V$$ $$32,000 \lt V$$ Which means that the home must be valued at a price greater than 32,000 dollars for the first tax bill to be a better deal than the second tax bill.
