Atheme park charges a flat fee of $500 for group bookings of more than 25 tickets, plus $20 per ticket for up to 100 tickets and $17 per ticket thereafter. if x represents the number of tickets sold under the group booking option, complete the limit equation that represents the average cost per ticket as the number of tickets purchased becomes very high.

The required equation is: [tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

Step-by-step explanation:

Consider the provided information.

Let x represents tickets sold.

A theme park charges a flat fee of $500 for group bookings of more than 25 tickets, plus $20 per ticket for up to 100 tickets and $17 per ticket thereafter.

The charges for booking 100 tickets will be:

[tex]500 + 20\times 100 = \$2500[/tex]

If you by more than 100 tickets theme park charges $17,

Thus, charges for x tickets will be = [tex]2500+ 17(x - 100)[/tex]

The limit equation represents the average cost per ticket as the number of tickets purchased becomes very high.

The Cost of one ticket of the theme park = [tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}[/tex]

Now solve the above limit equation that will gives you the average cost per ticket as the number of tickets purchased becomes very high.

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}= \lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}[/tex]

[tex]\lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}=0+17-0[/tex]

Hence, the cost per ticket is $17 as the number of tickets purchased becomes very high.

It's all about multiplication, 25 x 500 = 12,500 + 20 = 12,520 + 17,000, your answer is $29,520

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

Step-by-step explanation:

Let the theme park sold number of tickets = x

Theme park charges $500 for group booking more than 25 tickets.

In addition to this theme park charges $20 per ticket for up to 100 tickets.

So charges of 100 tickets = 500 + (100×20) = $2500

For more than 100 tickets theme park charges $17, so charges for x tickets will be = 500 + (100×20) + 17(x - 100)

= 2500 + 17(x - 100)

Cost of one ticket of the theme park = [tex]\frac{2500+17(x-100)}{x}[/tex]

Now we have to write the limit equation when number of tickets purchased becomes very high.

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}=17[/tex]

[By solving limit as below

[tex]\lim_{x \to \infty} \frac{2500+17(x-100)}{x}= \lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}[/tex]

since [tex]\lim_{x \to \infty}(\frac{1}{x})=0[/tex]

Therefore, [tex]\lim_{x \to \infty}\frac{2500}{x}+17-\frac{1700}{x}=0+17-0[/tex]

= 17 ]

it's all about multiplication,, your answer is $29,520

Step-by-step explanation:

25 x 500 = 12,500 + 20 = 12,520 + 17,000,

[tex]\lim_{n \to \infty} a_n \frac{2500+17(x-100)}{x} =17[/tex]

Step-by-step explanation: I got this correct on Edmentum.

[tex]Atheme park charges a flat fee of $500 for group bookings of more than 25 tickets, plus $20 per tick[/tex]