Final answer:
To find the number of additional windows for which the cost is the same at both companies, set up the equation $25 + $5x = $30 + $4x. Solving for x, we find that at 5 additional windows, both companies will charge the same amount.
Step-by-step explanation:
To determine how many additional windows would need to be installed for the price to be the same at both companies, we need to set up an equation where the total cost for company A is equal to the total cost for company B.
Let's denote the number of additional windows as x. The cost for company A will be the initial installation fee plus the cost for each additional window, which is $25 + $5x. The cost for company B will be their initial fee plus their charge for each additional window, which is $30 + $4x. Therefore, we can write the equation as:
$25 + $5x = $30 + $4x
To solve for x, we subtract $25 and $4x from both sides to get:
$5x - $4x = $30 - $25
$x = $5
This means that after 5 additional windows, the cost will be the same for both companies.