Question

In Washington DC, the tax on a property assessed at $890,000 is $14,240. If tax rates are proportional inthis city, how much would the tax be on a property assessed at $410,000?

Answer 1

Proportionality

Initial explanation

We have that the price of the properties and its tax are related:

price ⇔ tax

STEP 1: setting the relations

We have that $890,000 and its tax $14,240 are related:

$890,000 ⇔ $14,240

We want to find the tax of a property assessed at $410,000. This value and its task are related too:

$410,000 ⇔ ??

Then, we have that:

$410,000 ⇔ ??

$890,000 ⇔ $14,240

STEP 2: rates

If we divide both sides of the equation it will give the same result:

$\frac{410,000}{890,000}=\frac{?\text{?}}{14,240}$

STEP 3: solving the equation

Now we take 14,240 to the left side of the equation to find the tax of the second property:

$\begin{gathered} \frac{410,000}{890,000}=\frac{?\text{?}}{14,240} \\ \downarrow \\ \frac{410,000}{890,000}\cdot14,240=?\text{?} \end{gathered}$

Solving the operation:

$\frac{410,000}{890,000}\cdot14,240=6,560$

Then, the tax of the second property assessed at $410,000 is $6,560.

Answer: $6,560