We are given that Brianna needs to receive $199300 and that she also needs to allow for a 3 percent commission. Let "x" be the amount Brianna needs to sell her house. We need to subtract from this amount the 3% commission. To do that we will use the following relationship:
[tex]x-\frac{3}{100}x=199300[/tex]
Now, we solve for "x" first by adding the fractions using the following model:
[tex]a+\frac{b}{c}=\frac{ac+b}{c}[/tex]
Therefore, we will multiply the 100 from the denominator by "x" and subtract 3 from the result, like this:
[tex]\frac{100x-3x}{100}=199300[/tex]
Solving the operations we get:
[tex]\frac{97x}{100}=199300[/tex]
Now we multiply both sides by 100:
[tex]97x=19930000[/tex]
Now we divide both sides by 97:
[tex]x=\frac{19930000}{97}=205463.92[/tex]
Therefore, the amount is $205463.92. Since we are told to round to the nearest hundred dollars we round the answer to $205500.
