The cost of a single ticket depends on the number of tickets, *t*, purchased in a group, as represented by the function *C*(*t*).

*C*(*t*) = 

What is the total cost for 20 tickets?

$14.50

$16.00

$290.00

$320.00

To determine the total cost for 20 tickets, we first need to know the function $ C(t) $, which represents the cost of a single ticket depending on the number of tickets $ t $ purchased. Since the function $ C(t) $ is not provided in the problem, we'll have to infer it based on the given options.

Let's analyze the possible scenarios:

1. If the total cost is $ \$14.50 $, this would suggest the cost of a single ticket or a very small number of tickets, but not for 20 tickets.
2. If the total cost is $ \$16.00 $, this similarly suggests a low number of tickets, possibly just one or two.
3. $ \$290.00 $ and $ \$320.00 $ are more likely to be the total cost for 20 tickets.

Now, let’s try to reverse-engineer the cost per ticket from these options:

- If the total cost is $ \$290.00 $ for 20 tickets, the cost per ticket would be:
  \[
  \frac{290.00}{20} = 14.50 \text{ per ticket}
  \]
- If the total cost is $ \$320.00 $ for 20 tickets, the cost per ticket would be:
  \[
  \frac{320.00}{20} = 16.00 \text{ per ticket}
  \]

So, if $ C(t) $ represents the cost per ticket:
- $ C(t) = 14.50 $ would give a total cost of $ 20 \times 14.50 = 290.00 $.
- $ C(t) = 16.00 $ would give a total cost of $ 20 \times 16.00 = 320.00 $.

Since the problem asks for the total cost, the correct answer depends on the exact form of $ C(t) $, but with the given options, the total cost for 20 tickets is either $ \boxed{290.00} $ or $ \boxed{320.00} $. The most appropriate choice from the listed options is $ \boxed{290.00} $ as the total cost.

Do you have any further questions, or would you like additional details?

Here are 5 related questions for further practice:
1. If the cost per ticket decreases as more tickets are purchased, how would you model this in $ C(t) $?
2. How would the total cost change if there was a flat discount applied for purchasing 20 or more tickets?
3. What would be the total cost if only 10 tickets were purchased at $ \$14.50 $ per ticket?
4. If the cost per ticket is given by $ C(t) = 16 - 0.1t $, what is the cost for 20 tickets?
5. How does the total cost change if each ticket after the first 10 is discounted by 25%?

**Tip:** Always check if the cost function $ C(t) $ changes depending on the number of tickets or if it is constant across all ticket quantities before calculating the total cost.

Discover how to calculate the total cost for 20 tickets based on a cost function analysis. Explore scenarios where the cost per ticket varies and determine the appropriate total cost. Suitable for advanced high school students and beyond.

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