Question

The market price of a house is directly proportional to the total area of the house in square feet. If the price of a 1500 square feet home is $300000, what is the price of a 2000 square foot home?

Answer 1

The price of the house (y) is directly proportional to the total area of the house (x), you can express the relationship between both variables as follows:

`y=kx`

Where "k" is the constant of proportionality.

To determine the price of a house that has 2,000 ft², the first step is to determine the value of the constant of proportionality between both variables. For this, we have to use the known price and size of the house:

-The house has 1,500 ft² → this is the value of x

-The house costs $300,000 → this is the value of y

You can express the relationship as:

`\$300000=k\cdot1500ft^2`

To calculate the value of k, you have to divide both sides by 1,500ft²

`\begin{gathered} (\$300000)/(1500ft^2)=(k1500ft^2)/(1500ft^2) \\ k=200(\$)/(ft^2) \end{gathered}`

The constant of proportionality is 200$/ft², this value indicates that the price of the house increases $200 for every additional square foot.

Now that we know the value of the constant of proportionality we can calculate the price of a 2,000ft² house:

`y=200(\$)/(ft^2)x`

For x=2,000ft²

`\begin{gathered} y=200(\$)/(ft^2)\cdot2000ft^2 \\ y=\$400000 \end{gathered}`

The price of a 2,000ft² is $400,000