SAT Arithmetic Problem

Question

A total of $k$ passengers went on a bus trip. Each of the n buses that were used to transport the passengers could seat a maximum of $x$ passengers. If one bus had $3$ empty seats and the remaining buses were filled, which of the following expresses the relationship among $n, x$ and $k$?

Answer 1

If all the buses were filled, there would be $nx$ people on all the buses combined. Since three people are missing from the last bus, simply subtract 3. That number is the number of people who went on the trip.

Answer 2

First imagine all the buses were full. One bus has $x$ passengers, two buses have ??? $n$ buses have ??? Now deduct $3$ for the empty seats.

Answer 3

There are $k$ passengers.

One bus had 3 empty seats and the remaining buses were filled: So $(n-1)$ buses are filled, so there are $x$ passengers in $n-1$ buses, and at one bus there are $x-3$ passensers.

The sum of them is equal to $k$.

Therefore we have the folowing:

$$(n-1)x+(x-3)=k \Rightarrow nx-x+x-3=k \Rightarrow nx-3=k$$