Answer:
$90.
Explanation:
The given equation, f(x) = 50 + 20(x-1), represents the cost f(x) in dollars that a carpet cleaning company charges for cleaning n rooms.
Let's break down the equation to understand what it tells us about the carpet cleaning company:
1. The variable x represents the number of rooms being cleaned. The equation uses x-1 in order to account for the fact that the first room is charged at a different rate. This means that the cleaning company charges a different price for the first room compared to the subsequent rooms.
2. The constant term 50 represents the base cost for cleaning one room. It indicates that there is a fixed cost associated with the cleaning service, regardless of the number of rooms being cleaned.
3. The term 20(x-1) represents the additional cost for cleaning the remaining (x-1) rooms after the first one. The 20 represents the price per room, and (x-1) represents the number of additional rooms beyond the first one.
To illustrate with an example, let's say the company charges $50 for the first room and an additional $20 for each subsequent room. If you want to clean 3 rooms (x = 3), you would substitute x = 3 into the equation:
f(3) = 50 + 20(3-1)
= 50 + 20(2)
= 50 + 40
= 90
So, the cost for cleaning 3 rooms would be $90.
In summary, the equation f(x) = 50 + 20(x-1) tells us that the carpet cleaning company charges a base cost of $50 for the first room, and an additional $20 for each subsequent room.