Question

A sports trainer has monthly costs of $80 for phone service and $40 for his website and advertising. In addition he pays a $15 fee to the gym for each session in which he works with a client.
Required:
a. Write a function representing the average cost
b. Find the number of sessions the trainer needs if he wants the average cost to drop below $16 per session.

Answer 1

Answer:

Step-by-step explanation:

The average cost for the training session provided he is a sports trainer can be computed as follows:

Let's assume that;

average cost = C(x)

the no. of session = x

Then:

$C(x) = \dfrac{\text{Total cost}}{\text{no. \ of sessions}}$

$C(x) = \dfrac{\text{80 + 40 + 15x}}{\text{x}}$

$C(x) = \dfrac{\text{120+ 15x}}{\text{x}}$

Now, suppose the trainer wants the average cost C(x) to drop below $16;

Then, we have the following function:

$\dfrac{120+15x}{x}\leq C(x)$

$\dfrac{120+15x}{x}\leq16$

By cross multiply:

120 + 15x ≤ 16x

120 ≤ 16x - 15x

120 ≤ x

Therefore, the required no. of session, if the average cost should drop below $16, is 120.