Question

a city commission has proposed two tax bills. the first bill requires that a homeowner pay $1400 plus 3% of the assessed home value in taxes. the second bill requires taxes of $500 plus 6% of the assessed home value. what price range of home assessment would make the first bill a better deal for the homeowner? a home assessment greater than $\square$ would make the first bill a better deal.

Explanation:

Step1: Define variable for home value

Let $x$ = assessed home value (in dollars).

Step2: Set up cost equations for each bill

First bill cost: $1400 + 0.03x$
Second bill cost: $500 + 0.06x$

Step3: Set up inequality for first bill being cheaper

We need first bill cost < second bill cost:
$1400 + 0.03x < 500 + 0.06x$

Step4: Isolate variable terms

Subtract $0.03x$ from both sides:
$1400 < 500 + 0.03x$

Step5: Isolate constant terms

Subtract 500 from both sides:
$900 < 0.03x$

Step6: Solve for x

Divide both sides by 0.03:
$x > \frac{900}{0.03} = 30000$

Answer:

A home assessment greater than $\$30000$ would make the first bill a better deal.