Question

In a store, workers can serve 60 customers each hour on average. If x customers come to the store in a given hour, then the average number of customers C waiting in line C(x) = x^2/3600-60x where x<60. If 53 customers arrived in the past hour, there are approximately how many customers waiting in line? If there are 3 customers waiting in line, approximately how many customers arrived in the past hour?

Answer 1

Functions can be used to model real world situations.

• 7 customers are waiting in line, when 53 customers arrived in the past hour.
• 47 customers arrived in the past hour, When 3 customers are waiting in line

The function is given as:

$\mathbf{C(x) =\frac{x^2}{3600- 60x} }$

Where: x represents the number of customers

When x = 53, we have:

$\mathbf{C(x) =\frac{x^2}{3600- 60x} }$

$\mathbf{C(53) =\frac{53^2}{3600- 60 \times 53} }$

$\mathbf{C(53) =\frac{2809}{420} }$

$\mathbf{C(53) =6.688}$

Approximate

$\mathbf{C(53) =7}$

This means that:

7 customers are waiting in line, when 53 customers arrived in the past hour.

If C(x) = 3, we have:

$\mathbf{C(x) =\frac{x^2}{3600- 60x} }$

$\mathbf{3 =\frac{x^2}{3600- 60x} }$

Cross multiply

$\mathbf{3(3600- 60x) =x^2}$

$\mathbf{10800- 180x =x^2}$

Rewrite as:

$\mathbf{x^2 + 180x - 10800 = 0}$

Using a calculator

$\mathbf{x = 47.47\ or\ x=-227.48}$

x cannot be negative.

So, we have:

$\mathbf{x = 47.47}$

Approximate

$\mathbf{x = 47}$

This means that:

Read more about equations and functions at:

https://brainly.com/question/19221147