Question

Suppose a car rental company charges ​$148 for the first day and ​$98 for each additional or partial day. Let​ S(x) represent the cost of renting a car for x days. Find the value of ​S(6.50​).
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Part 1
A.
​$736
B.
​$785
C.
​$637
D.
​$687

Answer 1

To calculate the cost \( S(x) \) for renting a car for \( x \) days, we start with the charge structure provided:

- The cost for the first day is \( \$148 \).
- Each additional or partial day after the first day costs \( \$98 \).

When calculating the total cost for a rental period of \( x \) days, we note that:

- The first day always costs \( \$148 \).
- The additional days are calculated based on the number of days beyond the first one, and since \( x \) can be a partial day, the total number of days will always be the ceiling value of \( x \) days after the first day.

In this case, for \( x = 6.50 \):
- First day: \( \$148 \)
- Remaining days: \( 6.50 - 1 = 5.50 \) days

Since we charge for each additional day or partial day, we round 5.50 up to the next whole number. Thus, we essentially have 6 additional days to charge for.

Now we calculate the total cost \( S(6.50) \):

\[
S(6.50) = 148 + (6 \cdot 98)
\]

Breaking it down:

\[
6 \cdot 98 = 588
\]

Now, adding this to the cost of the first day:

\[
S(6.50) = 148 + 588 = 736
\]

Thus, the value of \( S(6.50) \) is \( \mathbf{736} \).

The correct answer is:
**A. $736**