CEMC Hypatia, 2021

The total cost to rent a car is $180.00.
If 4 people rent a car, the cost per person is $\dfrac{\$180.00}{4}=\$45.00$.
Since the members of the group equally share the total cost to rent the vehicle, the smaller the group, the greater the cost per person.

To rent an SUV, the smallest group size required is 5 passengers and the total cost is $200.00.
Thus, the maximum possible cost per person to rent an SUV is $\dfrac{\$200.00}{5}=\$40.00$.
Let the total cost to rent a van be $v$.

When renting a van, the maximum possible cost per person occurs when the number of

passengers is 9 (the fewest number possible), and so this maximum cost is $\dfrac{v}{9}$.

The minimum possible cost per person occurs when the number of passengers is 12 (the

greatest number possible), and so this minimum cost is $\dfrac{v}{12}$.

Then, $\dfrac{v}{9}-\dfrac{v}{12}=\$6.00$ or $\dfrac{4v-3v}{36}=\$6.00$, and so $v=\$6.00\times36$.
Thus, the total cost to rent a van is $216.00.