Question

A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the amount of carpet installed.

Answer 1

Given:

• The base rate charged by the carpet installer = $$40$
• Rate charged by the carpet installer for labor = $$1.50$ per square foot.
• The total cost of labor depends on the amount of carpet installed.

To find:

To express the total charges for a work as a function of the amount of carpet installed.

To be recollected:

Function: Function is defined as the relation of each input of one set which are independent to each input of other set which are dependent. This is explained as follows:

Let '$x$' be a domain input of one set. It's function is denoted by "$f(x)$", which is equal to an input of other set and is called as co-domain.

Answer:

As per the given data,

• The base rate charged by the carpet installer is $$40$.
• The rate of labor = $$1.50$ per square foot of carpet installed.

Let the amount of area of the carpet installed be "$A$" square feet.

Now, the total cost of labor is given by $$1.50(A)$.

Let the total cost of work done be denoted by "$C$".

Now, the total cost of work done is given by:

$C=40+1.50(A)$

Final answer:

∴ The total cost of a carpet work as charged by the carpet installer is given by the equation:

$C=40+1.50(A)$