Questions: Winter visitors to Mt. Washington in New Hampshire can travel up the mountain in a specially designed snow vehicle. A group of 105 visitors goes on the snow-vehicle tour. Each tour vehicle can transport 9 visitors. How many vehicles will be needed for all of the visitors? 105 divided by 9 equals 1 of 5 QUESTIONS The remainder to this problem shows that if there are 11 snow vehicles, The total number of vehicles needed for all visitors is

Solution Steps

To determine how many vehicles are needed to transport all 105 visitors, we need to divide the total number of visitors by the capacity of each vehicle, which is 9. Since we cannot have a fraction of a vehicle, we will round up to the nearest whole number if there is any remainder.

To find the number of vehicles required to transport all visitors, we use the formula:

\[ \text{vehicles\_needed} = \lceil \frac{\text{total\_visitors}}{\text{vehicle\_capacity}} \rceil \]

Substituting the values:

\[ \text{vehicles\_needed} = \lceil \frac{105}{9} \rceil \]

Calculating this gives:

\[ \text{vehicles\_needed} = \lceil 11.6667 \rceil = 12 \]

Next, we find the remainder when dividing the total number of visitors by the vehicle capacity:

\[ \text{remainder} = 105 \mod 9 \]

Calculating this gives:

\[ \text{remainder} = 6 \]

Since the remainder is 6, this indicates that if there are 11 vehicles, 6 visitors would still need transportation. Therefore, we need a total of 12 vehicles to accommodate all visitors.

Final Answer