Hamadi is renting a car. The rental charge is $\$ 17.50$ per day plus $\$ 0.16$ per mile. Hamadi can spend at most $\$ 33$ for the cost of the car rental. If Hamadi rents the car for one day, which of the following is one possible number of miles Hamadi can drive the rental car? $\newline$ Choose $1$ answer: $\newline$ (A) $53$ $\newline$ (B) $97$ $\newline$ (C) $\mathbf{1 1 0}$ $\newline$ (D) $\mathbf{1 5 0}$

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Q. Hamadi is renting a car. The rental charge is

\$ 17.50

per day plus

\$ 0.16

per mile. Hamadi can spend at most

\$ 33

for the cost of the car rental. If Hamadi rents the car for one day, which of the following is one possible number of miles Hamadi can drive the rental car?

\newline

Choose

1

answer:

\newline

(A)

53

\newline

(B)

97

\newline

(C)

\mathbf{1 1 0}

\newline

(D)

\mathbf{1 5 0}

Determine total cost: Determine the total cost allowed for the car rental. $\newline$ Hamadi can spend at most $\$33$ for the car rental.
Calculate one-day cost: Calculate the cost for renting the car for one day without considering the miles driven. $\newline$ The rental charge per day is $\$17.50$ . $\newline$ Total cost for one day = $\$17.50$
Subtract rental charge: Subtract the one-day rental charge from the total allowed cost to find out how much is left for the mileage charge. $\newline$ $\$33 - \$17.50 = \$15.50$ $\newline$ This is the amount Hamadi can spend on the mileage charge.
Calculate maximum miles: Calculate the maximum number of miles Hamadi can drive with the remaining $\$15.50$ . The charge per mile is $\$0.16$ . Maximum miles = $\frac{\$15.50}{\$0.16}$ per mile Maximum miles = $96.875$ miles
Round down to whole number: Since Hamadi cannot drive a fraction of a mile in this context, we round down to the nearest whole number. $\newline$ Hamadi can drive a maximum of $96$ whole miles.
Compare with given choices: Compare the calculated maximum miles with the given choices. $\newline$ The closest choice that does not exceed $96$ miles is (A) $53$ miles and (B) $97$ miles. However, since Hamadi cannot exceed $96$ miles, option (B) $97$ miles is not possible.