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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.

Respuesta :

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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:

[tex]C(x) = \dfrac{\text{Total cost}}{\text{no. \ of sessions}}[/tex]

[tex]C(x) = \dfrac{\text{80 + 40 + 15x}}{\text{x}}[/tex]

[tex]C(x) = \dfrac{\text{120+ 15x}}{\text{x}}[/tex]

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

Then, we have the following function:

[tex]\dfrac{120+15x}{x}\leq C(x)[/tex]

[tex]\dfrac{120+15x}{x}\leq16[/tex]

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.

Following are the solution to the required points:

  • Assuming that he's also a sports trainer, the typical cost of such a training program is just as follows:

        Total cost = C(x)

        Total session = x  

Then:

[tex]\to C(x)=\frac{\text{Total cost}}{\text{Total sessions}}=\frac{80+40+15x}{x}= \frac{120+15x}{x}[/tex]

  • Assume the trainer desires that the average cost C(x) be less than $16. So function is therefore available:

[tex]\to \frac{120+15x}{x} \leq C(x)\\\\\to \frac{120+15x}{x} \leq 16\\\\[/tex]

By cross multiply:

[tex]\to 120 + 15x \leq 16x\\\\\to 120 \leq 16x - 15x\\\\ \to 120 \leq x[/tex]

As a result, if the average cost drops below $16, the required number of sessions is 120.

Learn more:

brainly.com/question/24859268

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