Question

on your own

1. a desert tour includes 305 people traveling by van. each van can transport

18 people.
a. estimate the number of vans needed.
b. construct arguments is it an overestimate or underestimate?
in this situation, would it be better to overestimate or underestimate?
explain your choice.

Explanation:

Step1: Calculate the number of vans

We use the formula \(n=\frac{N}{c}\), where \(N = 305\) (total number of people) and \(c=18\) (capacity of each van). So \(n=\frac{305}{18}\approx16.94\).

Step2: Determine the nature of the estimate

Since we cannot have a fraction of a van and all 305 people need to be transported, we must round up. If we were to underestimate (round down), there would be people left without a ride.

Answer:

A. The number of vans needed is \(\lceil\frac{305}{18}
ceil = 17\) (using the ceiling function to round up).
B. It is an over - estimate. If we were to underestimate (e.g., say 16 vans), \(16\times18 = 288\) people would be transported, and \(305 - 288=17\) people would be left. So, in this situation (transporting all people), overestimating (rounding up) is better.