Question

# Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two

Modeling
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A city commission has proposed two tax bills. The first bill requires that a homeowner pay $1800 plus 3% of the assessed home value in taxes. The second bill requires taxes of$200 plus 8% of the assessed home value. What price range of home assessment would make the first bill a better deal?

2021-06-16

Let's note: x the price of a home assesment
We write the inequality modelling the problem: $$1800+0.03x<200+0.08x$$
We solve the inequality: $$1800+0.03x-0.03x<200+0.08x-0.03x$$
$$1800<200+0.05x$$
$$1800-200<200+0.05x-200$$
$$1600<0.05x$$
$$\frac{1600}{0.05} =32,000$$ The solution is: $$x>32000$$