Question

the monthly rent for an 800 square foot office is $975. For an 1100 square foot office, the rent is $1125. Write and solve a linear equation to find the monthly rent for a 1500 square foot office.

Answer 1

For 300 more square feet the rent is $150 more.
Rent per additional square foot is 150/300 or 0.50.
For an additional 400 square feet the rent is an additional 400(0.50) or $200.
The rent for 1500 feet squared office is $1325.

Answer 2

$1325

Explanation:

Given :

The monthly rent for an 800 square foot office is $975.

For an 1100 square foot office, the rent is $1125.

To Find : Write and solve a linear equation to find the monthly rent for a 1500 square foot office.

Solution:

We will form the equation using two points equation formula

`(x_1,y_1)=(800,975)`

`(x_2.y_2)=(1100,1125)`

Formula :
`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Substitute the values

`y-975=(1125-975)/(1100-800)(x-800)`

`y-975=0.5(x-800)`

`y-975=0.5x-400`

`y=0.5x-400+975`

`y=0.5x+575`

So, a linear equation to find the monthly rent is
`y=0.5x+575` where x is the square feet and y is the monthly rent.

Now we are supposed to find the monthly rent for a 1500 square foot office.

Substitute x = 1500

`y=0.5(1500)+575`

`y=1325`

Hence the monthly rent for a 1500 square foot office is $1325 .