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} (y_1)/(y_2)=(kx_1)/(kx_2) \\ \text{ Simplifying:} \\ (y_1)/(y_2)=(x_1)/(x_2) \\ \text{ Dividing by x1 at both sides} \\ (y_1)/(y_2\cdot x_1)=(x_1)/(x_2\cdot x_1) \\ (y_1)/(y_2\cdot x_1)=(1)/(x_2) \\ \text{ Multiplying by y2 at both sides} \\ (y_1\cdot y_2)/(y_2\cdot x_1)=(1\cdot y_2)/(x_2) \\ (y_1)/(x_1)=(y_2)/(x_2) \end{gathered}`

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

`(19530)/(930000)=(x)/(660000)`