Question

In Atlanta, the tax on a property assessed at $930,000 is $19,530. If tax rates are proportional in this city, how much would the tax be on a property assessed at $660,000?Choose the proportion you would use to solve the problem.

Answer 1

Variables

• x: assessed price

,

• y: tax

Given that the tax is proportional to the assessed price, then these variables are related by the next formula:

y = kx

where k is some constant.

If we have two ordered pairs (x1, y1) and (x2, y2), the relations are:

$\begin{gathered} y_1=kx_1 \\ \text{ And} \\ y_2=kx_2 \end{gathered}$

Dividing y1 by y2:

$\begin{gathered} \frac{y_1}{y_2}=\frac{kx_1}{kx_2} \\ \text{ Simplifying:} \\ \frac{y_1}{y_2}=\frac{x_1}{x_2} \\ \text{ Dividing by x1 at both sides} \\ \frac{y_1}{y_2\cdot x_1}=\frac{x_1}{x_2\cdot x_1} \\ \frac{y_1}{y_2\cdot x_1}=\frac{1}{x_2} \\ \text{ Multiplying by y2 at both sides} \\ \frac{y_1\cdot y_2}{y_2\cdot x_1}=\frac{1\cdot y_2}{x_2} \\ \frac{y_1}{x_1}=\frac{y_2}{x_2} \end{gathered}$

Substituting with y1 = $19,530, x1 = $930,000, x2 = $660,000, and y2 = x:

$\frac{19530}{930000}=\frac{x}{660000}$